So does the theory that each time we die we play as another Booker been validated in any way?
It still doesn't make sense to me. If this was the case then there would have been only one attempt at the whole thing (in which they just brute force the whole thing by "calling in another" Booker each time one dies), and it is confirmed that there have been many ( the Luteces dialogue on the boat confirms this)
This isn't necessarily the case because every new Booker would have to do the same thing to make things easier to change, hence there being many Bookers by the end of the game.
So for example:
Booker 1: Action A, Action B, Action C, dies.
Booker 2: Action A, Action B, Action D, Action E, Action F, dies.
Booker 3: Action A, Action B, Action D, Action E, Action G, Action H, Action I, dies.
Booker 4: Action A, Action B, Action D, Action E, Action G, Action H, Action J, Action K, Action L, Action M, dies.
Turns out action M is related to Action B, so they need to change action B!
Booker 5: Action A, Action V, Action D, Action E, Action G, Action H, Action J, Action K, dies
Turns out Action V got Booker killed:
Booker 6: Action A, Action W, Action D, Action E, Action G, Action H, Action J, Action K, Action L, Action M, Action N...
...
Booker 123 (Booker we play as by coin flip): Action A, Action W, Action D, Action E, Action G, Action H, Action J, Action K, Action L, Action M... Action Q dies in firefight.
Booker 124: Action A, Action W, Action D, Action E, Action G, Action H, Action J, Action K, Action L, Action M, Action R... Action S, dies in firefight.
Booker 125: Action A, Action W, Action D, Action E, Action G, Action H, Action J, Action K, Action L, Action M, Action R... Action S, dies in the same firefight again.
Booker 126: Action A, Action W, Action D, Action E, Action G, Action H, Action J, Action K, Action L, Action M, Action R... Action P... Action Z. Success (so we experienced/played through everything this Booker did)!
So by the 126th (this is just an example) time, they'll have repeated almost everything, exactly the same; having the row conversation every single time, very slightly meddling. The game just fast forwards to the point before where we died for convenience. We also know many Bookers died at Songbird's hand. By the time we play through the game, they've done everything so much times, spent so long trying to reset timeline, that it's hard to take everything so seriously, as it could just be another failure. They don't 'brute force it' by bringing in another Booker exactly where the previous one died, they brute force it by repeating everything exactly the same (and then the player manages to allow Booker to survive by doing better).
EDIT: MMBosstones86 explained it much better/easier to understand I think.
EDIT: Although as Trigger mentions, the mandatory office sequences haven't been 'resolved'. Personally, I think it's much more likely they're flashbacks/memories while Sorian believes that they're deaths.