So if I want to improve the world, it makes sense for me to care about "my own" ... well-being - even though future instances of "me" are actually distinct systems ... because A) I care about the well-being of minds in general, and B) they share at least part of my goals, and are thus more likely to carry them out.

I think it's clear that there is also terminal value in caring about the well-being of "me". As with most other human psychological drives, it acts as a sloppily optimized algorithm of some instrumental value, but while its purpose could be achieved more efficiently by other means, the particular way it happens to be implemented contributes an aspect of human values that is important in itself, in a way that's unrelated to the evolutionary purpose that gave rise to the psychological drive, or to instrumental value of its present implementation.

(Relevant posts: Evolutionary Psychology, Thou Art Godshatter, In Praise of Boredom.)