It's interesting how difficult it is to make sure that we're all talking about the same thing here.
There's no difficulty. Which is to say, it's not a matter of two reasonable parties groping for common ground. It's a matter of you constantly trying to foist your predetermined beliefs as if they were facts that others had to explain, and a subsequent matter of your critics correctly not letting you do it. You seem to think your critics can't see the rather obvious game you're trying to play here.
I think that you do experience what I'm calling a "sense of self"
Yes, self-aware beings are self-aware. But you insist on ambiguous language rather than precise language, so that you can equivocate agreement to one facet as agreement to all the nonsense you read into it. Not gonna happen, so stop insulting everyone by trying. Every time you try this, all your critics catch you, every time. It's high time you gave your critics their due for having successfully refuted your proof -- several times over.
and, that you do know/understand which shared experience it is that I'm referring to.
Yes, self-aware beings are identically self-aware, regardless of what cause they attribute that self-awareness to.
In a statistical inference, E is the same data for hypothesis H as it is for ~H, or for some other hypothesis K. E must be formulated as an observation, such that it doesn't involve disagreements about its nature or cause. You are unable to do this. You have formulated E so that it contains conjectural causes from ~H, and it is those causes that you want H to explain, not the observation. You simply don't know how to correctly formulate a statistical inference and are not interested in learning.
You and I just disagree about its nature.
Equivocation. "Nature" can mean either the holistic view of something's observable behavior, or it can mean its underlying cause. Since those nuances live on both sides of the gap in this argument, you don't get to insist on it to fuel your equivocal strategy. We stipulate that each person subjectively experiences self-awareness in substantially the same way as everyone else. That aspect of its "nature" is agreeable.
We vehemently disagree that the underlying cause of it under materialism is anything like the soul you're frantically trying to cram into the materialist model. In materialism, self-awareness is an emergent property of a functioning brain. You've already conceded that your version of materialism in your P(E|H) estimate is not actually materialism. Why you're still flogging a conceded argument and groveling for agreement after proudly admitting to a straw-man approach is beyond anyone's comprehension.
Do you accept that conclusion?
Not if that conclusion means accepting your ongoing attempts to make self-awareness equivalent to a soul. Which it almost certainly does, so no I don't accept your conclusion. Please stop asking people to agree to your conclusion as a prerequisite for having the debate.
Your inability to separate the different elements of a statistical inference is one of several individually fatal flaws I've identified in your argument, and which you clearly have no interest in thinking about. Explain again why anyone should take you seriously.