The only way the ending made sense to me was to have this Booker going to Columbia before he gave up Anna, and the baptism normally happens after he gives her up. If he leaves in this window, the ending makes sense. The only problem is, Elizabeth mentions he spends 20 years in his apartment regretting giving up Anna, until someone gives him a chance to make it right. If there was a concrete timeline it would help, but the game is fairly vague when it comes to this. Which must be intentional, given how much detail is everywhere else.