I care about living (usually), but it's not clear to me that what I care about when I care about living is absent in the "failed" scenario.

As far as I can tell, "being me" just isn't all that precisely defined in the first place; it describes a wide range of possible conditions. Which seems to allow for the possibility of two entities A and B existing at some future time such that A and B are different, but both A and B satisfy the condition of being me.

I agree, though, that if A is the result of my body traveling through time in the conventional manner, and B is the result of some other process, and A and B are different, it is conventional to say that A is really me and B is not. It's just that this strikes me as a socially constructed truth more than an empirically observed one.

I also agree that the test you describe is compelling evidence that the copy/recreation process is as reliable a self-preserver as anything could be.