This has indeed been discussed
before, though I was regrettably unable to participate there.
I would generally agree that
LOTR and its associated works are not wholly Christian. Tolkien, being familiar with a wide variety of myths and legends, as well as being a devout Catholic, certainly poured elements of different traditions into his story, and those knowledgeable in those respective elements will tend to see them, sometimes even when they aren't really there.
That said, your assertion that that the "one God" aspect is missing from the stories is, I think, incorrect.
Eru Ilúvatar is the Prime Creator in the mythos. All that is, including the "divine" Valar and Maiar, were created by him. The Valar are the "governors" of Arda; their task to see that Ilúvatar's will and purposes are served. The same could be said for the "angels" of Christianity. The duties of the latter are also to serve the One God, though they do not take an active role in the "governance" of our world, according to the Bible.