should feel like [...]

Interesting that you put it this way, rather than "should think that". If indeed the Sequences say "should feel like", I agree with them. But if they say we "should think that" the copies are the same you, that's mistaken (because it either violates transitivity of identity, or explodes so many practices of re-identification that it would be much better to coin a new word).

A few words on "feel" and "like": by "feel" I take it we mean both that one experiences certain emotions, and that one is generally motivated to protect and enhance the welfare of this person. By "like" we mean that the emotions and motivations are highly similar, and clearly cluster together with self-concern simpliciter, even if there are a few differences.