(Please pardon me for overly iterating certain points while explaining. I needed to in order to get my thoughts all in order.)
Close but not quite the full answer. I'm also going to start with some things that are not quite the answer to your question, but I need to cover these bases before answering in the next part.
As you know, Okabe was able to get his hands on the IBN5100 in the 0.5710..% world lines. However, his death like you said is determined to happen from 0-0.99….% in 2025 and not before. In fact, the convergence that has a hold on his death in this attractor field is so strong that when SERN tests for the existence of world line convergence after they have captured Okabe and co. in 0.334581% in the short story The Distant Valhalla (Somewhat of a SPOILER, highlight to read) [by shooting at Okabe at close range not a single one of the bullets is able to kill him.]
However, it should be noted that D-Mails are unable to completely "ignore" convergence, strictly speaking. Wherever a D-Mail causes you to shift to, the effect of the D-Mail is part of the convergence of the world line you arrive in. But, D-Mails are capable of causing a big enough change to bring you to a different attractor field altogether. Take for example the D-Mail from the Faris Ending in the visual novel, it would cause a shift to the Omega AF -0.275349% or the D-Mail from the Hyde of the Dark Dimension drama CD, which causes a shift to Gamma 2.615074%. Coincidentally, that D-Mail is enough to avert Okabe dying in 2025, because in the Gamma attractor field he is still alive in 2036, terrorizing Japan as its dictator Hououin Kyouma.
Let's review a bit what Suzuha had to say,
So, the way I understand it from the events we see depicted in the original visual novel, attractor fields are like gigantic world lines and the reverse is also true; world lines are like small attractor fields, which is why Mayuri always dies on the evening of the 13th in 0.337187%, even though she dies in multiple ways as Okabe tries to save her and even though the Attractor Field Alpha's world line convergence only demands that she die sometime in August, 2010. So, how does that work?
We know that Okabe's Reading Steiner is only triggered by -and the divergence meter he invented can only measure- changes in the world line fluctuation rate, the divergence, up to the sixth decimal place. Any smaller than ±0.000001% and he won't notice the world shifting lines. What's more if the change is small enough even others can notice the change made.
Take for example, the gelbanana experiments and the first "so-and-so is stupid" D-Mails that were sent after they first discovered the PhoneWave was a time machine. More concretely, think of the first D-Mail that Okabe sent when he tried to undo Moeka's D-Mail. Since the D-Mail failed to change Moeka's past actions, Okabe felt no change in the world line, and the divergence meter animation that we the audience see when the world line changes did not play. Also, Kurisu who was helping him, still completely remembered helping him send the mail.
However, that is still going from a world line in which Moeka had not received the D-Mail from Okabe, to one in which she had. -The D-Mail just did not have the effect that Okabe wanted because she had lied to Okabe about what she wanted her D-Mail to change.-
Suzuha says, "Countless possible worldlines exist side by side, branching out to infinity."
So for example, let's say within the measurement of 0.000000% there could be micro world lines like
0.00000099999999999…. and on to infinity%
0.000000009032743028…. and on to infinity%
Confused? Think of 0.337187% again, the world line where Mayuri always dies in the evening of the 13th. However, Okabe time leapt multiple times and she ended up dying in multiple ways. Those are all smaller world lines. Let's indicate them as 0.337187…%.
The full bundle of world lines in an attractor field share a point of convergence. The world lines of Attractor Field Alpha are converging to a SERN Dystopia. The world lines of Attractor Field Beta are converging to WWIII. Those I'll term Large Divergence Points/points of convergence.
The attractor fields Alpha and Beta are themselves, on a larger level converging to the world's population being culled to 1 billion. Greater than a Large Divergence Point, let's call that a Major Divergence Point -Thanks to the admin of the now defunct ibm500.net SG wiki for the naming.-
This would be the Major Divergence Point of the PhoneWave time machine, which Alpha, Beta, Delta, and Epsilon all converged to.
Then there are the world lines from 0.000000% to 0.409…% where Faris's father always lives. Let's call that a Medium Divergence Point.
Under that you could have a Minor Divergence Point,
Imagine that you are at a café and you are trying to decide if you want to order coffee or tea. There is plenty of tea leaves and coffee beans in stock. There is absolutely no special consequence to your decision. However, at the moment, the world is on a world line where you are supposed to order coffee but you order tea instead. Congrats you just caused the world to change micro world lines. :) This is why even though the world lines demand certain things, it is not pure determinism.
If you are aware due to time travel and an ability like Okabe's of the world line/attractor field's convergence restraining you then you can make conscious decisions to try to change things. If you are not aware then the world might be moving and drifting through world lines anyway as the billions of people make their billions of decisions, though it would be very rare that any of those decisions or their butterfly effect would be enough to make a ±0.000001% difference to the divergence rate of where the world is at. -Which is why Okabe never felt his Reading Steiner activate from the time he gained it, which is hinted to be due to a fever in 1999, up until he sent the D-Mail about Kurisu's death.-
In answer to your question, I think that convergence happens at all levels of an attractor field and its world lines. It is just a matter of the more major a divergence point is, in other words the more world lines that in a bundle converge to this outcome, the more drastic the effect of your choices has to be to change to a world line not effected by that particular point of convergence -i.e., either diverging to a different outcome at that point or not leading to that point at all because it already diverged at some earlier point in time-. And, that is why it seems more difficult to escape something that the attractor field is converging to than something that only a portion of its world lines are converging to.
Put another way, the more world lines that converge to an outcome the more difficult it is to reach a different outcome because your actions may just lead to the same overall result with the only difference being the way in which that result is reached, i.e. the different ways that Mayuri dies and the different ways in which the IBN5100 does not reach the lab. The difficulty with changing Mayuri's determined death in August 2010 and Okabe's in 2025 is that they happen on such a macro scale that it is difficult to see what their causes are except that it is the Alpha attractor field.
Note 1: Emphasis on, it is the effect of your choice that needs to be drastic and not so much the choice itself. Example, deleting three chopped up emails about Kurisu dying with future send date time stamps from SERN's database is, depending on one's perspective, arguably less drastic a move than Okabe gutting himself in order to fake Kurisu's death. However, the effects of these choices are equally drastic, causing the world to shift out of an attractor field, because SERN noticing the first D-Mail is the trigger, the cornerstone if you will, for the SERN dystopia to become a reality as the future of the Alpha AF, while Kurisu's death is the trigger or cornerstone for WWIII to occur in the Beta AF.
So, I have been using both "divergence point" and "point of convergence" interchangably as equal terms that just describe different parts of the same phenomenon while explaining. It should be noted that a point of convergence, where two or more world lines converge to, is simultaneously a point of divergence where other world lines diverge away from them. Even world lines that do converge, diverge immediately after. That's why I'm adopting the term "divergence point".
Take 2000 as an example, in 2000 the Alpha, Beta, Omega, Delta, and Epsilon AFs converged to Y2K not happening, while the Gamma AF diverged to Y2K occurring -At the same time it was probably converging with some other as-yet-unnamed attractor fields in which Y2k also occurred.
Hopefully, what I explained in the above section has helped clear up for you a bit the limitations upon a time-leaper in changing an event, but I'll try to give a more in-depth explanation of time leaping in case it helps. Like you seem to already understand, a time leap does use much of the same mechanics as a D-Mail. In a nutshell, it is sending your compressed memories like you would a D-Mail. Only it makes a phone call that sends signals that cause you to download/remember your future memories instead of sending chunks of text to your phone for you to read.
A time leap phone call can actually be sent to someone else's phone -or your phone can be picked up by someone else-, but the predicted results are disastrous.
For the sake of making an easy to read diagram, lets pretend that world lines are perfectly straight and lined up side by side. Like this, from what we've been shown so far, successful time leaps are not able to travel very far sideways.
When time leaping multiple times in 0.337187…% in the original VN and anime, Okabe will always end up in the past of 0.337187…%, so his attempts to save Mayuri are always restricted by the convergence of 0.337187…% for her to die on the evening of the 13th. However, the D-Mail to not stop Suzuha that he sends from 0.337187…% gets received in 0.409431%, which causes the world to shift to that line. This works because not stopping Suzuha counts as a Medium or Minor Divergence Point, where the world can cross from one measurable world line to another with a significant difference in outcome.
As explained before, a D-Mail, depending on the contents and the receiver, can have a small enough effect to not change the measurable world line. If Okabe had sent a "Christina is baka" D-Mail, then he would have still stayed in 0.337187…% with only a grumpy assistant as a change. However, sending a D-Mail to not stop Suzuha from leaving on the 9th caused enough changes from that Medium/Minor Divergence Point onwards that 0.337187% and 0.409431% -and many other world lines- shared, for it to be a difference of considerably greater than ±0.000001% causing the world to change to that different, measurable world line, 0.409431%, which coincidentally determines Mayuri's death to not occur on the 13th.
So, time leaping is restricted by the technology that Kurisu has at the time she makes it in the original VN to 48 hours.
If we only look at the evidence that is presented in the original novel then time-leaping always sends you back in time to the same measurable world line that you leaped from. In that case, it would make no difference even if Okabe time-leaped to July 28th, because it would be the July 28th of the Alpha attractor field. The D-Mail that got caught in SERN's database in the Alpha AF was sent from the Beta AF. On July 28th in the Alpha AF, Suzuha crash landed in the Radio Kaikan Building which caused Kurisu to not die, which caused Alpha Okabe to not send a D-Mail at that time. He was then overwritten by Beta (Active) Okabe instead.
So far in the whole Steins;Gate franchise there is only one example -at the beginning of the "Three Contrapasso About The Abduction" story in Steins;Gate: Linear Bounded Phenogram- of a time leap phone call being received outside of the measurable world line that it was sent from, and that is also not only an example of a time leap to another attractor field, but an example of a failed time leap as well.
If I remember correctly, Epsilon Kurisu theorizes that the time leap failed because of the modifications they had made to the PhoneWave. However, this is an incorrect hypothesis that she makes due to lack of information. From Okabe's lack of memories about events in the Epsilon AF, his memories corresponding with the Alpha AF, and the fragments of memories he has but does not understand of his experiences in repeated time leaps in Aug. 13th, 0.337187…%, we know that he time leapt from Alpha, and a time leap is not run through the time leap machine again of the world line where it is received, so any modifications made to the PhoneWave in Epsilon would not matter a jot to it.
So, no, I don't think it would be possible for Okabe to, under most circumstances, change attractor fields (successfully) via a time leap, which is similar to how physical time travel in a time machine seems to always be bound to the attractor field you jump from, even though D-Mails are proven to be easily received across attractor fields. One of the most curious things...
Earlier in this conversation I told you, "Also, it should be noted that it is not just Okabe who 'jump[s] from one attractor field to the other' the whole world changes to a different world line in a different attractor field. Okabe is, however, aware of this shift when it occurs unlike others due to his Reading Steiner ability."
This holds true when talking about the world changing from one active world line to the next active world line. However, in the alternative endings in the original visual novel and in the spin-off material, we do see Okabe's memories being sent -due to his Reading Steiner(?)- from an active world line to an inactive one or from an inactive one to another inactive one, when sending D-Mails, etc. Now, inactive world lines are all just "possibilities that exist simultaneously", so as far as the main story and its active world line -currently the Steins Gate- is concerned, this doesn't really matter. -Inactive world lines can effect active ones, but we've only seen that happen via physical time travel, i.e. Suzuha from 0.000000% landing in the active Alpha world lines.-
Why exactly would sending a D-Mail from an active or inactive world line to an(other) inactive world line cause the memories and personality of the Okabe from the world line the D-Mail was sent from to be sent as well is still unclear -to me at least-, but I think, we know it happens even in the main story. Okabe from Beta sent the D-Mail about Kurisu dying, this caused his memories to be sent to the Okabes across all of the Alpha AF, even to the world lines that did not immediately become the new active world line. We know this because -Correct me if I'm remembering wrong.- when Okabe starts drifting through the Alpha world lines, past the Alpha world line he first arrived in, it is clear from what the other labmems say that his self had been talking about his Reading Steiner ability already, or calling Christina a zombie, etc. before his "active" self arrives in that world line. Also, there is the very fact that 0.000000% Okabe and Daru were able to reason that the D-Mail about Kurisu's death was the key to getting out of the Alpha attractor field, which info got passed onto 0.000000% Suzuha, who passed it on to the Active Okabe. 0.000000% Okabe would probably not have be able to reason that out if he did not have the memories of being the Okabe who sent the D-Mail, I believe.
I had forgotten about this conversation that Suzuha, Okabe and Kurisu have later in chapter six of the VN, until just before I was about to post this. So, I'll just tack this onto the end. It basically has them discussing quite a few things we have covered.