Conners, I've been thinking about this and I'm less convinced than I was of the utter separateness of science and religion. But I'm still not sure I agree with you. For me, if science were to start trying to evaluate religious and metaphysical claims it would have to go through such a revolutionary change that I don't think it would really still be science. You seem to be saying that all the questions we can ask should eventually be either answered or revealed as meaningless. I think that although we can't tell where the precise limits of science might be, there is a definite limit to the kinds of question that science can ask or hope to answer (or even dissolve).
I've heard scientists making claims that many branches of knowledge will eventually become part of science. For example, Edward Wilson argues in 'Consilience' that all sorts of things, including stuff like literary, philosophical and cultural studies, will eventually be scientific. (IIRC). This can be pretty baffling and tends to confirm my theories that scientists reveal their own naivety when they blunder into disciplines. He should stick to the bees, methinks. Theology is a more borderline case because it sometimes make claims that initially seem to belong in the same sort of area as cosmology, say.
I agree that what seems theoretically unfalsifiable/untestable today can become falsifiable eventually - for example, if I remember right many of Newton's astronomical theories made predictions that were unfalsifiable at the time but which could later on be tested when measuring equipment had improved.
However, I think that you are not taking into account something fundamental about what religion is supposed to be. Would a God who could be probed and tested in double-blind controlled experiments be a god at all in any real sense of the word? If Dawkins woke up in heaven, then the truth behind the universe would presumably not be something that could be explained to him discursively - God could perhaps tell him a bit more about science, and this would be the sort of thing we could have discovered anyway, the sort of thing any other scientist could have explained to him just as well. But any real religious experience of seeming to understand how and why it all works, of direct experience of the divine, might well not be something that could be communicated in words or equations.
Seems to me that perhaps the most basic question of religion is 'Is this all there is?' Is the universe we experience through our senses the only dimension of existence, or are there more mysterious levels of existence? If I ask this question, surely science is fated always to reply 'I don't know if this is all there is. But here's some more of it. And some more! And more!" How can it get beyond the world of experience? Often all it has to offer is occam's razor - just saying that as our experience is all we have, we should avoid believing in stuff outside our experience. But what we experience is determined by the sensory organs we find ourselves equipped with...
But I'm neither particularly religious nor a scientist, and I admit that it could well be that all sorts of claims that we now think of as religious will one day be either disproven or revealed as meaningless. I suppose it comes down to whether or not you think the universe's ultimate nature is intelligible to the human mind.