I guess at this point we're just going to have to agree to disagree. I think you don't give science enough credit. You are absolutely right that it is only within the capabilities of science to disprove, however, just because the discipline is humble enough to know we can never claim something with 100% certainty, doesn't mean we can therefore dismiss those things we know with 99.99% certainty. There is vastly more to this universe that is yet to be discovered compared to the little we currently understand, but that does not change the fact that we do know a lot.
I just don't see any reason to believe that the human experience surpasses bodily existence, as you put it. There is absolutely no evidence to even suggest this be the case, and there is no natural need
for it. Here we return to Occam's razor: you'd have to significantly over complicate nature to fit this in, and it's completely unnecessary.
You are right that we don't yet fully understand the nature of consciousness, but why does this spur you on to think that it might be something beyond biology?