Your reasoning is sound, but the game is LITERALLY telling you what it is. The quote at the very start of the game states:
"The mind of the subject will desperately struggle to create memories where none exist..."
Barriers to Trans-Dimensional Travel
That line does not rule out a theory of time travel, nor do any of the others that I can find from my recordings list in game. None of the quotes you have given me do, either.
From my stance, Elizabeth and Booker's pursuit of killing Comstock leading to the baptism scene coupled with strong inferences that their act there influenced all future events and probabilities is stronger evidence to me. This evidence suggests that both time travel and cross dimensional travel takes place in this game.
To convince me, you'd have to construct an argument with evidence which supports the idea they only ever move perpendicularly with respect to time from the universe they are in before going through a tear to the universe after such.
I've got something for you, but I can't write it now becuase of that GDC live video thing on, but I think it might satisfy you. Think of Comstock and his rapid aging for now.