Replying to myself is weird, but this is a bit of an aside.
This is a problem that can plague time travel games - if the PCs substantially change history, the GM needs to rewrite the history each time, which is kind of a pain.
Thus, most games are about maintaining the timelines, so if the PCs win, you don't need to rewrite history much.
Well, there's no actual answer to that in physics. So, as a game designer, what do you want to do with it? Maybe it just sucks that you don't know the new timeline - perhaps after repeated trips, you don't know what you should change, becuse your knowledge of history is out of date.
This is a problem that can plague time travel games - if the PCs substantially change history, the GM needs to rewrite the history each time, which is kind of a pain.
Thus, most games are about maintaining the timelines, so if the PCs win, you don't need to rewrite history much.