Nonetheless it's important to attend to these "better-defined" parts of you, because that's where we start to get away from the big distraction created by the freedom to self-define. This flexibility in the notion of self is mostly about what you get to include and exclude. So there's a large collection of "potential self-parts", but the potential self-parts themselves don't exist just by definition; they are the actually existing raw material in terms of which a definition of self gets its meaning - these are a part of me, those are not. There has to be an objective account of what these "parts" are, in terms of the wavefunction ontology, and it ought to say unambiguously whether or not they "split".
I'm not clear on what you mean by "self-parts" here, but I'm assuming you mean something like basis states that contain people like you, which you can describe people in terms of. In which case I've already trodden this ground - no such objective account must necessarily exist, but such things can be useful, though you still wouldn't be able to get any two different peoples' idealized algorithms to agree on the edge cases.
http://www.scottaaronson.com/blog/?p=1103
Eliezer's gung-ho attitude about the realism of the Many Worlds Interpretation always rubbed me the wrong way, especially in the podcast between both him and Scott (around 8:43 in http://bloggingheads.tv/videos/2220). I've seen a similar sentiment expressed before about the MWI sequences. And I say that still believing it to be the most seemingly correct of the available interpretations.
I feel Scott's post does an excellent job grounding it as a possibly correct, and in-principle falsifiable interpretation.