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?
As just a single example, Sir Roger Penrose, noted collaborator of Professor Stephen Hawking, has proposed a very radical hypothesis in his book The Emperor's New Mind.
In that book, he argues that consciousness derives in part from a fundamental process in quantum mechanics known popularly as the collapse of the wave function, and he further argues that theoretical physics, as it presently stands, is inadequate to explain consciousness. A summary in Wikipedia can be found here
While I do not agree with a lot of what Sir Roger has to say on the matter, I do agree that the explanation of consciousness may well require new physical theories. If new physical theories are required, then we simply have to wait for the dust to settle, in order to hear what science has to say on what exactly consciousness is. We therefore have to wait at least that long to hear all it has to say about human nature. That's all I'm saying, and I've certainly never said that I believe in life after death.
How you get from that, to me not giving science enough credit, I haven't a clue.