One remark just for your interest. It's uncanonical, and I am not saying anyone should believe it, or not even that I would promote it, Eru forbid. But it may be interesting for this discussion, I think, to mention it. The idea was in the LotR RPG made by the Iron Crown Enterprises (if anyone is interested, I think it was done in early 90's, if ever, the particular volume was called "Over the Misty Mountains" or something like that).
Anyway, there was a (non-player) character of a Maia who was a servant of Varda, she was named Kalamírë (i.e. "light-jewel") and she was the personification of Rainbow. It is said there that she was a "light-spirit" and she had always either the form of rainbow, or the form of a young girl, generally dancing in the place where the rainbow touched the ground. She could simply "jump" between places far away from each other (possibly by the rainbow?) if on both places there were both light and water in the air. "Legends tell of places where the stars shone so bright that the rainbow appeared even at night". It was said that she usually "with childish joy flickers from a tear in clouds over the Misty Mountains to another, which floods the Shire with sunshine, and then back to the flow of rain lashing Mirkwood. Wind, rain, raging elements cheer her up. She dances everywhere she comes, and spreads rainbow light, as long as the sun shines through the rain drops in the air." Her role in the story was that she could take with her anyone who touches her, and she carried the heroes of the story to Anduin:
"...her voice, clear as bell-sound. 'Should I take you on the road through the sky? Around the sun and the clouds? With the wind and the birds? I will take you to Anduin! Take my hands!'"
I think this "Rainbow spirit" was very Tolkienesque and if it were an option for how to explain rainbow in M-E, I won't see a problem. But if so, then I could maybe see this Maia with the dual-nature of serving both Varda and Ulmo (or at least a little bit, given the undeniable, and even emphasised, connection with rain), and overall her character reminded me of Goldberry quite a lot (which could have been intentional) and also of Vána (see Valaquenta). Of course, the interpretations of rainbow can be many, also, as it was mentioned, simply as something like a sign (a variation of Varda's sign of Valacirca to Morgoth?) or just a normal effect of water (and light), like the snow or rain itself. But as I said, I thought you might like reading about that, and eventually it could also bring you to some new thoughts
