Time travel stories like this always screw me up, and to be fair I didn't play the game, I just lurked around threads like this and combined that with what I already knew.
I think Elizabeth is able to see and manipulate tears because her physical being is present in two different worlds. Her finger is in the Booker reality, and the rest of her is in one of the many Comstock realities. So, at the end of the game when the Elizabeths kill Booker and then disappear.... how could they drown him without them existing in the first place? That means that atleast one Dimension voyaging Elizabeth still needs to exist and one timeline needs to be maintained in order for the cycle to carry out. I guess they had this idea for a really long time considering they had a "Days of the Future Past" cover in one of the game magazines.
That one dimension is the original time line where all the other possibilities sprang from. In essence, drowning Booker during his baptism wasn't actually... drowning him. The priest for one isn't in the scene, and nobody else is, either, so it's not a time travel thing. It's just Booker being drowned by all the variants of Elizabeth from the possible worlds that Comstock was alive in. Before cutting to credits, the scene lingers on Booker and Elizabeth, and we don't see Elizabeth blink out like her variants. The baptism/drowning, I think, is Booker confronting and letting go of what happened at the Wounded Knee Massacre, which is what drove him to seek salvation in the first place. Booker Who Would Become Comstock didn't ever really let go of it and that's what the baptism was supposed to do and indeed does for a lot of Born Again types. It's a metaphorical aid to wash away the person you were to become the person you want to be. You know, with way more Jesus and God and shit. Instead of washing away the sin (because Booker/Comstock couldn't shake it off) it instead drove him to evangelical, doomsday preaching, to building Columbia, to bringing about another "great flood" like the Noah's Ark story in order to rid the world of the Sodomites and monsters like he used to be/still is. Booker DeWitt on the other hand rejected salvation and saw himself as a monster for what happened, and so he went on to do more monstrous things (Pinkertons didn't fuck around y'all) which led to him selling his child to get rid of gambling debts.
Basically what the drowning was meant to represent, I think, is Booker killing the past and letting it go. He's seen where it leads and he hates who he becomes in both instances. So in a way he's still being "born again," but this time he's actually letting go and the man who comes up for air won't be the same Booker we played as, and it won't be Comstock either.
Now for Ridiculous Speculation: I took the post credits scene to mean that Booker would be okay, that he had Anna (his wife still died in childbirth), and that he was a better man than he used to be. The kind of man that won't sell his goddamn child, for instance. It's not perfect, as his wife is still dead and he's no doubt still traumatized by the Wounded Knee Massacre, but he didn't abandon Anna this time, which is what set the events of Infinite in motion.
I could be totally wrong about all of this, though. That was my read on the characters and themes present in Infinite. It goes to some really dark places, but at the end I think it's actually incredibly optimistic and it's kinda sweet.