The rest of your interpretation is great too. As a lover of Bombadil, and the River-Daughter, I am comfortable with just letting him be whatever he is. But I am impressed with your ability to allow for vagueness! Your reputation as a strict historian now has to make room for "I don't know and it doesn't really matter". Hi! Ho! Merry Dol!
I wonder if there's such a thing as a doctorate in Tolkienology? I wonder what my parents would say if I said I wanted to study such a thing...