So, bicker and speculate about TTI this and TB that as we may, I have a feeling the developers didn't create the game with those things in mind, which pretty much makes all of those arguments pointless... x_x
They most certainly did not, I'm sure. But, they created a coherent story in which time paradoxes and time duplicates do not exist. So whether they intended to have TTI or TB or not, they (or something very much similar to them)
have to be present to account for the lack of paradoxes.
Just for fun, try to create a simple time travel story yourself in which paradoxes and duplicates do not exist (using the canon explanation of sending futures to the DBT every time time travel occurs). You can't do it without TTI or TB or something very, very similar. Somehow past versions of time travellers have to be removed and present versions have to be preserved. Otherwise the entire story would fall apart.
So I think it's safe to say that we can have a good discussion about the ending of Cross with TB and TTI firmly in place. Otherwise we can't have a meaningful discussion at all.
That said, the question of whether or not dimensional travel is covered by TTI is a good one. But remember, Dalton came from 12000 BC and eventually ended up in 1000 (or so) AD. Regardless of whether or not he did dimensional travel as well, his appearance in 1000 AD should still be covered by TTI.
But just for fun let's try to figure out whether or not it would be necessary to cover dimensional travel by something like TB and TTI (DB and DTI perhaps?). I've never done it before so it should be interesting. I'll make a simple thought experiment and see if dimensional travel creates paradoxes. Here we go:
Two dimensions exist which are parallel to each other in time. In Dimension 1 a man called Dimensional Traveler exists in the timeline. In Dimension 2 he was never born. A person called Time Traveller was born in Dimension 2 and may or may not exist in Dimension 1 (doesn't matter).
Dimension 1: Time X: Dimensional Traveller goes to dimension 2 via some dimensional gate.
Dimension 2: Time X: Dimensional Traveller appears in dimension 2. Time Traveller meets Dimensional Traveller, decides he is an asshole, and travels first to Dimension 1 with the intent of going back in time to kill his grandfather so he never exists.
Dimension 1: Time X+1: Time Traveller arrives in dimension 1, goes back in time to X-100.
Dimension 1: Time X-100: Time Traveller kills Dimensional Travellers grandfather, changing history in Dimension 1 so that Dimensional Traveller never crosses the dimensions to Dimension 2, then travels back to the present in Dimension 1 and goes back to his home dimension of Dimension 2 at Time X+2.
Dimension 2: Time X+2: Time Traveller returns to his home dimension anticipating that Dimensional Traveller wouldn't be there. Does he meet Dimensional Traveller, or not?
Quite a thinker, eh?
EDIT: I have reinstated my conclusion that dimensional travel is covered by "Dimensional Bastard" and "Dimensional Traveller Immunity". It would have to be, as in my example a paradox would occur. One might think that the paradox would be taken care off by the actions of Time Traveller being preserved by TTI alone, but his original dimensional crossing to Dimension 1 would have to be preserved as well.
Thanks for the thought provoking thread!