A distinctive element in Leverage episodes is how we see the cons backwards. We see how it plays out, and things look like they're going badly, and then we see flashbacks of the hidden preparations that our heroes made earlier on -- sometimes new scenes, sometimes extensions of scenes we already saw -- which mean that it's actually going well. Maybe even according to plan.

To simulate Leverage in an RPG without this element would be basically like playing any modern con-artist-driven suspense. But is there a game where you could play it like the episode itself -- where the story plays out, and then the players make up flashbacks which retroactively change what happened earlier, to change how what's currently happening is going to play out? Something with some guidance on how to encourage the players to make really Leverage-like flashbacks, but still limiting them enough so that it's a challenge and they have to be creative and appropriate, and do in flashbacks only things that they realistically could have planned ahead (within the broad suspension of disbelief of this show, I mean).

I would strongly recommend the trick of flashback planning.

Don't lay out the whole plan at the start. Offer the first obstacle, plan how to overcome it, play through the plan. Then flashback to the planning table for the second obstacle, play through that. Repeat as needed.

If required, you might need one of the PCs to be carrying a suitcase or pack, which will have always held whatever they later decide they need for the obstacles in their flashback planning sessions.

This helps prevent wasting three hours planning, just to blow it all in one bad roll.

This trick gives the illusion of having planned brilliantly for many different contingencies without wasting hours and hours planning.

Then if you choose to follow the normal formula for such heists, there will then be something unforeseen, which they could not have planned for (or their information is wrong). At this point they need to think on their feet.

Another useful trick is to have a soft fail option. Most heists are fragile or brittle. Just one bad roll, just one mistake, and the whole thing fails, alarms go off, guards arrive, buildings lock down. All bad.

So try to add a soft fail that complicates without ruining everything. For example, the PCs fail a stealth roll and get spotted. Rather than having them seen by a guard or setting off an alarm, have them seen by another thief who is also breaking in. Both need to avoid the guards and alarms, but having competition makes it that much more complicated. The rival thief may even set off the alarms if the PCs look like they are going to win.

Another soft fail might be getting logged by a sensor. It doesn't set off an alarm, but if the PCs don't deal with it, then it may lead back to them later.