Just finished it tonight and done some reading to try and get things straight.
One thing I'm not certain on is the timeline for anna being born, is she born before or after the baptism. If it's before then what happens to anna in comstock timeline? It makes more sense that booker goes on to have anna after failing to get baptised, I'm not sure what the truth is though.
To me it makes the most sense that at the end elizabeth is simply putting you in the shoes of the prior booker, you experience handing over anna, and then later trying to chase her down leading to her finger getting sliced off, I think these sections are your original memories coming back to you (that was genuinely earlier in your own timeline)
Near the end booker doesn't know who elizabeth is shortly before drowning. That would suggest something more than just dimension hopping, more like time travel...thats where it gets a little fuzzy for me.
But it seems that in the infinite universes there is a whole series of bookers and elizabeths working towards the same goal and at least some of them make it as far as you do because you see them crossing the wooden bridges near the end having the same conversation as you're having. To me that suggests that they all lead their versions of their bookers to the same spot...
In which case the ending very much feels like all the successful bookers kind of amalgamate at the end (there's an elastic term for you!), and sort of come together at one point in space/time, there's only one fate for booker at that point and you witness it first person but there's multiple very slightly different elizabeths which is why several hold you down.
Eliminating comstock eliminates him taking elizabeth and such returns the timeline to just being a drunk booker before he sold anna. The ending is obviously meant to be ambiguous deliberately in the same way inception was, in some respects it doesn't really matter that much, as far as I'm concerned those things are a bit of a cheap trick to just generate interest and talk about the game post completion, I suspect that it's just meant to be left open to the interpretation, i'd personally like a happy ending where Anna is alive and booker gets his shit together but unless someone finds a reason to positively identify what happens, or Ken steps forwards and clarifies I'm just not going to waste my time on it.
Fantastic game though, GOTY for 2013 without a doubt and squarely in my top 5 of all time best single player games, very probably my fave ever singleplayer FPS.