>You're really talking about (at best) a new instantiation of the identical consciousness in a new body. That's not the original consciousness moving, that's a new (identical) consciousness coming to life.

This is making a lot of assumptions about how consciousness works. If I make a copy of a book the story doesn't move, but it is now in two places. If I destroy the original book the story isn't lost. I think experience might be more like that. Multiple copies of the same information system will all only have one subjective experience.

Yes if you run two versions they will diverge and the question is much more complicated. But if there is one moment of copy/destruction or you're scanning and then simulating/rebuilding a frozen brain, then there's no point in time where a consciousness doesn't have a future version.