It seems to me that you are trying to recover the properties of conscious experience in a way that can be reduced to physics. Ultimately, I just feel that this approach is not likely to succeed without radical revisions to what you consider to be conscious experience. :)
Generally speaking, I agree with the dualists who argue that physics is incompatible with the claimed properties of qualia. Unlike the dualists, I see this as a strike against qualia rather than a strike against physics. David Chalmers does a great job in his articles outlining why conscious properties don't fit nicely in our normal physical models.
It's not simply that we are awaiting more data to fill in the details: it's that there seems to be no way even in principle to incorporate conscious experience into physics. Physics is just a different type of beast: it has no mental core, it is entirely made up of mathematical relations, and is completely global. Consciousness as it's described seems entirely inexplicable in that respect, and I don't see how it could possibly supervene on the physical.
One could imagine a hypothetical heaven-believer (someone who claimed to have gone to heaven and back) listing possible ways to incorporate their experience into physics. They could say,
Hard-to-eff, as it's not clear how physics interacts with the heavenly realm. We must do more work to find out where the entry points of heaven and earth are.
In practice private due to the fact that technology hasn't been developed yet that can allow me to send messages back from heaven while I'm there.
Pretty directly apprehensible because how would it even be possible for me to have experienced that without heaven literally being real!
On the other hand, a skeptic could reply that:
Even if mind reading technology isn't good enough yet, our best models say that humans can be described as complicated computers with a particular neural network architecture. And we know that computers can have bugs in them causing them to say things when there is no logical justification.
Also, we know that computers can lack perfect introspection so we know that even if it is utterly convinced that heaven is real, this could just be due to the fact that the computer is following its programming and is exceptionally stubborn.
Heaven has no clear interpretation in our physical models. Yes, we could see that a supervenience is possible. But why rely on that hope? Isn't it better to say that the belief is caused by some sort of internal illusion? The latter hypothesis is at least explicable within our models and doesn't require us to make new fundamental philosophical advances.