I have no idea if this is what you are looking for, but I'll take a crack at it. First off, I think we have to make a distinction between the Science of Middle-Earth, and the Science of our time. In Middle-Earth, we have Balrogs, Wizards, talking swords, talking spiders, of course none of these are "scientific" or "proven" in our own time. However, they are "proven" in Middle-Earth. So, I think we have to look at the "Science of Middle-earth," and talk about it within the books/fantasy style realm, not within our own view, of that Balrogs don't exist.
I think to answer the questions between "Science" and "Magic" we have to look at Galadriel's words in "Mirror of Galadriel."
Quote:
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"And you?" She said, turning to Sam. "For this is what your folk would call magic , I believe; though I do not understand clearly what they mean; and they seem to use the same word of the deceits of the Enemy."
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To Galadriel, the Mirror of Galadriel, isn't magic, to non-magical beings (Sam) it is. For something that can't be explained by humans, we term it "miracle," or "magic." However, Galadriel isn't familiar with this term. So, to her, the Mirror of Galadriel isn't magic? Is it science? Let's look at some other Elvish items, The elven-cloaks, lembas, Miruvor. These too, would be considered "magical." But, Galadriel would term it something else. Again, is this science? Did the elves, examine, study, come up with water, food, cloaks, to feed and replenish the body, or to discover a form of invisibility?
P.S. I hope that's what you are looking for.