I thought about Looper's time travel and I think I have a solution to the disfigurement/vanishing problem. Introduce a form of 'quantum entanglement' between future and present loopers. Here's how it works:
Old Seth jumps back in time. He now occupies the same 'moment' as Young Seth. Since they are basically the same person, they're almost identical on a atomic level (not 100% because one is older but this isn't Time Cop so it doesn't matter). We can nitpick and say that the body recreates different cells at different speeds etc but the bottom line is: there's enough young seth in the future version to make this work.
Now. Old Seth runs away, Young Seth gets captured. They put him on a table and blow his hand off with a shotgun or something. This doesn't cause the Future Seth to suddenly lose a hand but the atoms in his hand respond to what happens to their 'younger' counterparts. His arm starts breaking down on a molecular level mimicking what would happen to you if you tried to play baseball with a piece of a fuel rod from a nuclear reactor. This only works through space and not time so nothing is going to suddenly vanish from existence and create all sorts of continuity problems. That way you can still have a scene where Old Seth is racing through the city while falling apart and still make sense.
As for the ending:
Young Joe blows his head off = Old Joe's brain melts and he collapses instantly.
This setup also makes Joe's decision to kill himself more reasonable since Old Joe could've still managed to pull the trigger before his hand fell apart. A headshot would be the only way to go.
The only drawback of this magic bean is that you'd have to specify that the link only works one way. Otherwise the whole Looping business wouldn't work at all. (Well, that's not exactly true, you can still make it work but I haven't figured out a way around that problem without altering the structure of the movie).
I hope this makes sense 