I'm not one to really call movies perfect, I think most have at least a thing or two that can be fixed. That being said, I really enjoyed the Prestige and don't really, on a personal level, think it needs to be changed, but by all means go for it! More power to you.
I did, however, just want to post to offer a word of warning: you have some pretty ambitious ideas there. Again, not necessarily a bad thing, but trust me, this fan-editing shit ain't so easy. Case in point, these past few days I have been working on just a personal fan-edit for myself, of which I thought would be rather easy to do so. Well, it isn't that easy. Just making simple cuts and rearrangements was stupidly hard, and I can't even really imagine trying to change around whole plot elements. This all culminated in a GREATLY increased appreciation for the talent and motivation that the great fan-editors possess (I'm looking at you Phantom Editor, MagnoliaFan, Adywan and ADigitalMan). Looking at your profile, I see you joined recently, but that doesn't really have any bearing on what skill level of editing you have. So all I'll say is simply to make sure you stay in your skill range, or you will get very frustrated. Very. Haha
So again, absolutely go for it. I don't want to discourage you at all, and despite the lack of responses so far, I think many others would be intrigued if you make good work on this front.
Lastly, of the four potential ideas you listed out, 3 and 4 are the best. I don't know how the hell you'd do them, but that's where your own creativity comes into play. Have at it
O and props on the USA pride avatar. Love it