Grin. You agreed and then disagreed. I think you are right in both cases because Tolkien is not using direct theologically precise symbols or direct allegory but may have created more than he realized in a Christian context. When Lewis gained Tolkein’s agreement to write direct allegories of Christianity, Lewis as Science Fiction, Tolkien as fantasy, Lewis promptly wrote the Perelandra series. Tolkien promptly wrote . . . nothing. I think Tolkein used up what he had to say in LOTR, he exhausted his imagination with that eruption, whether he knew it or not.
The genesis of Middle-Earth came about as a way of making a concrete history to place his created languages in, and then just kind of took on a life of its own.
His histories and short stories of Middle-Earth can be found in not just his three novels (The Hobbit, The Lord of the Rings, and The Children of Hurin), but in The Silmarillion, The Book of Lost Tales, and The Histories of Middle-Earth edited by Christopher Tolkien.
Lewis created the World of Narnia in his novels. Tolkien set The Lord of the Rings in Middle-Earth, a completely constructed world outside of that one story.
And that is why Tolkien's theology is infused in the story in a more subtle, and yet thorough, way than Lewis could have accomplished.