I think Mithalwen has one of the keys to this mystery.
I also think it worthwhile to distinguish between the Elvish Arts and Dark Sorcery. The former the Elves did not even name "magic", whereas the latter were not called "magic" either, but sorcery. Is there reference to the Dark Arts in the ouvre?
The "Mouth of Sauron" delved in sorcery, says Tolkien somewhere, thus his long years, I think.
A ring to explain Beorn shape shifting? I doubt it. I think, again, it's too mechanistic an approach to the way Tolkien did his myth making. If you look at his mythic sources, there were shape shifters aplenty and they needed no ring.
As for the lesser rings, is not the template is the Silmarils rather than anything Sauron might contrive? Thus, it requires that the Elves must take from either themselves (their own spirits/fea), or take something from nature/Arda and form it into a ring. So perhaps anything that something from nature could do, they made their "trifle" rings to be able to do?
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