This one is seriously long. I appologize in advance. I started this last night and finished it today after writing and re-writing. This the best I came up with:

I just rewatched the Martinez parts of the season and this is what I put together. I apologize in advance because e it is really long. (Note: I started this last night and It was so big, I emailed it to myself to edit and post.)

Martinez initially thought Ben was following him in their first meeting. So, he wasn't looking to stop Ben at all at that point.

He was willing to work for Magic and do any mission asked, no questions asked. When Magic visited him in 2022, which is before he leapt.

On the battleship, he told Ben that he would win. Win what? Be the first to get to Ben’s target destination?

When Janis came back in to the picture during the mental hospital episode, she said Ben had 3 chances to stop Martinez before Martinez kills Addison. The hospital was the last chance. If he couldn't stop Martinez, then Ben was to sacrifice himself to stop Martinez. In this case it was to prevent the girl from getting saved which would prevent both from leaping and they both would be stuck in the past.

When Ben is stabbed, Martinez said his orders were to stop Ben before they crossed again. That implies that someone is working with Martinez. The funny thing about that is we don't see the helper, which is strange because Martinez can see Addison. So is it because we're not meant to see who is helping or is it because there is no one and Martinez leapt just before the meltdown and was told to stop Ben by the third meeting or else Martinez will fail his mission? Then again 1st episode Ben who leapt was told about Martinez because he told Janis that he had 3 chances to stop Martinez. But Martinez wasn't surprised to see Ben and knew about Ben so how can that be?

I got the pacifist part wrong before. He was calling Ben a pacifist. Which ties into when Martinez was talking to Addison, he said he was there to do what Ben couldn't. I'm assuming his mission is this. But he could also of meant he was there to save the girl because Ben couldn't. Probably purposely written to be vague by the show’s writers to cause more mystery and confusion.

One thing to note is that in the hospital, he told Ben that Ben sabotaged his initial plan to save the girl. Does that affect anything? Is that the only sabotage that Ben needed to do? While the girl is saved, he technically did sabotage Martinez. Playing devil’s advocate, Ziggy predicted that Martinez had a 10% chance of saving the girl on his own. Maybe Ben had to get there to sabotage Martinez’s plan because it failed initially and the girl was lost.

Ian said around episode 5 that Ben was using Quantum gravity to jump further and further. And that maybe Ben wasn't trying to get to the past. He's trying to get to the future. Why would he do that or how would he know he needed to get there?

Ok so let’s go wild and start trying to work everything out.

Ben is now supposedly in the future. We don't know if it is the very distant future or the near future. We assume it's distant because Ian appears to be much older. He’s waited for Ben for a long time. We also assume this is Ian in the future. But we really don’t know yet. It could be Ian leaping into someone in the future. If he figured out Ben was leaping to the future then he could also figured out how to meet him there too. Ben would see him as Ian if he was Ian himself or if Ian was a leaper. Also, if Ian was a hologram.

We assume the meltdown is because of Ben because the writing so far is making it seem that way. It can be the result of anything really because we don't know the date he’s at. He might not even be the future. If it is a nuclear winter, the radiation fall out could be messing with ben’s quantum signature and that’s why they couldn’t find him. Remember, Martinez never said that he had to stop Ben from ending the world. He just said he had to stop Ben before they crossed paths again.

So how did we get to this point? If the meltdown is the future and it’s the result of the project then what I the order of events.

My guess, original timeline is Addison was the original leaper and she dies. Her death causes some disaster to happen because she died, or her death doesn’t stop it from happening. Now the military steps in and takes over and sends Martinez. His mission could be finishing Addison’s mission or helping Addison. He could have failed or succeeded, either way the world is worse off so Ian has to go back and warn Ben. Doesn’t explain why He wasn’t surprised about Ben leaping. The only way I can see for this to fit is that Martinez leaps after Ian did. I’m thinking that Maybe Ian knows Martinez was going to leap (for finish Addison’s/help Addison reason? Completely new reason?) and figured out that if Martinez succeeds then disaster will strike.

Ian leaps and warns Ben before Martinez can. Of course, that wouldn’t go unnoticed so now Martinez knows he needs to get there first. Which the idea of getting there first is stupid because time travel can be to seemingly specific point so one just needs a spot just before the other. But this is TV. As he progresses, his handler thinks that Ben is no threat at first then realizes that Ben needs removed/stopped during the Mental hospital episode. That could be why Martinez waits till then to try and kill Ben. Something happens and we end up at meltdown. Maybe Martinez succeeds and destruction ensues. Maybe he fails and the world is worse off. Maybe the meltdown is deliberate destruction of Ziggy which is nuclear powered and causes a nuclear winter. Could even be Ziggy fighting back to not be shutdown permanently? If Ziggy’s the mole does that mean he’s alive and wants to stay alive? Does ben “arrive too late” and has to leap again to fix that? The bigger question is when leaps into the meltdown aftermath, is he walking out of the imaging chamber? If he leapt into someone who was in the chamber, who was it? Also how did Ian see it was Ben if he wasn’t also a leaper. He had no reason to think it was Ben at all. Not yet at least. And did anyone notice that both Ben and Ian are wearing Imaging chamber outfits under their “coats”? If I’m right about the outfits then Ben didn’t leap into the future, he leapt home.

Humor me and let’s assume I’m right. Ben leapt home. Maybe this was his destination all along and he was too late. Or maybe whatever Martinez did, caused the meltdown. Now what? Do Ben and Ian work together using the old 1st generation Ziggy/accelerator/chamber to send Ian back in time to tell Ben to leap using different info? If so, then maybe Ian didn’t leap before Martinez and Martinez leaps in the relative future to the start of the series. While doing his mission, Martinez and probable handler come across Ben and they use Ziggy to figure out that Ben is out to stop him for an unknown reason. Maybe in that timeline where Ben had not leaped, it was Ben who opposed Martinez’s mission and Martinez assumes Ben’s there to stop him and leapt somehow which is why he wasn’t surprised. They can’t stop him because they needed Ben for Quantum leap to function like u/bros402 said. It weirdly fits now.

Of course, there is one more possibility. What if the final destination was set to be the plane in the last episode? And they needed that leap to get ben to return home after the meltdown? It was the only way to ensure Ben lived to survive the disaster because in the original timeline ben dies in the meltdown. He knew all along that if he didn’t stop Martinez at the third point in time then he would have to go to the future to hopefully be able to build another system so he could go back and try to stop Martinez again. If he had stopped Martinez in the 3rd meeting, then he would have been able to leap back home. But he didn’t’ so he has to sacrifice himself as the last ditch effort by going into the future and hoping there was a way for him to go back and fix things. That was the only way to ensure Ben survives but there was no guarantee he would survive the future, or be able to go back in time again or anything really. That means maybe Ian was the one to leap at the last second before meltdown to go back and do the warning. When he comes back it is also post disaster as well.

It's all highly complicated and probably all full of shit, but the last theory works better than everything else. All the stuff up to the 3rd meeting fits. Ian is the last minute leaper in this case. Ben and Addison die in the original line. Martinez caused the meltdown. Ian goes back to warn Ben to get him to stop Martinez or else they meet in the distant future to try again.