I don't see an issue with having two yous that are nonetheless separate people from eachother, that's actually exactly what I think would happen in such an instance. Asking which is "you" would be like watching a cell undergo mitosis and then asking which one is the original cell. Continuity mattering seems like a problem to me because it feels like it should require involving something outside the material universe to make it make sense. I'm not sure how best to explain this, but it seems to me that:
- you exist, for obvious reasons, since you perceive yourself
- you aren't everyone and everything
- the previous two things should mean that there is something about what you are that makes it, you, and not someone else, nor some unconscious zombie
If that thing, whatever it is, is part of the material universe, then the perfect copy must have it too by definition, it wouldn't be a perfect copy if there was something materially different about it, and then it would have to be you, because it has whatever that thing is that makes it "you". If that thing exists but is not present in a physically identical copy, then wherever it exists must be outside the physical universe, yet capable of some kind of interaction with it (since presumably you cease if killed materially). That isn't logically impossible, but requires adding an entire layer to reality to make it make sense, which seems premature when other interpretations don't require this (and we could end up in the same boat anyway, if I made a thought experiment that suggests some really advanced technology has found a way to manipulate this other layer too, and copies you there as well) Continuity (for anything, not just humans) by itself isn't really a "thing". It isn't made of anything, and doesn't seem to interact with the physical world in any measurable way. As far as I can tell, it requires making fewer unproven assumptions about how the universe works to assume that continuity is merely a concept we made up due to the manner in which we perceive time, without any actual physical validity to it.