- Is this "self" the same concept/experience that reincarnationists think returns?
No.
First let's get something out of the way. You're not even trying to hide your equivocations anymore. Every time you use one of these -- "/" -- you try to sneak multiple ambiguous concepts past your critics. It's the difference between "Jabba" and "Jabba/child-molester." In other words, a big important difference. Your critics are kind enough to use single words. They're kind enough to use specific words. They're kind enough to supply you with the definitions of words they're using, where there's the possibility of misunderstanding. So kindly stop trying to back-door inappropriate concepts into the argument by slash-gregating them together as if your critics should take them as one lump sum.
Now back to no. It's no because you're trying to make one side's explanation (~H, there is an immortal soul) part of the data (E, a person has a sense of self) such that all the hypotheses would have to explain that
cause, not just the effect. It's one of the fatal flaws we all know you can't answer. Fatal Flaw #3 describes how you don't know the different parts of a statistical inference and can't properly tell what role each one plays. You've just posted more evidence that you persist in flawed reasoning.
The datum E is the sense of self. The data cannot include any sort of explanation for how they came about. ~H (or more properly, perhaps some hypothesis in ~H) wants to explain E by means of a separately-existing immortal soul. That would be evaluated under P(E|~H). H, materialism, explains E as an emergent property of the process of consciousness, which proceeds in a functioning human brain. That is what you're trying to reckon as P(E|H). H is not responsible for trying (and, you hope, failing) to explain a cause that ~H proposes.
As for "reincarnationists," I have to march behind Loss Leader's flag on this one. You clearly haven't done anything to determine what, if anything, the various believers in reincarnation actually believe or what they might, if anything, have in common. So there's a separate justification for a "no" answer in the form of your not having defined the target.