I am reluctantly someone who pretty much doesn't care about what happens after I die. This is a position I that I don't necessarily endorse, and if I could easily self-modify into the sort of person who did care I would.

I don't think this makes me a monster. I basically behave the same way as people who claim they do care about what happens after they die. That is, I have plans for what happens to my assets if I die. I have life insurance ("free" through work) that pays to my wife if I die. I wouldn't take a billion dollars on the condition that a third world country would blow up the day after I died.

As you say, though, it's "me-of-the-present" that cares about these things. With the self-modification bit above, really what I mean is "I'd like to self-modify into the sort of person who could say that I cared about what happens after I die and not feel compelled to clarify that I really mean that I think good things are good and that acting as if I cared about good things continuing to happen after I die is probably a better strategy to keep good things happening while I'm alive."