The Moon! What Moon?!

[Galin]

Christopher Tolkien notes that Ainulindale C* Round World Version was:

'...thus an experiment, conceived and composed, as it appears, before the writing of The Return of the King, and certainly before The Lord of the Rings was finished. It was set aside; but as it will appear later in this book, it was by no means entirely forgotten.' Morgoth's Ring

In Ainulindale C* (in which the Sun was not a Tree-flower) Melkor took a portion of the earth and this became Ithil, and its origin is placed in the context of the tumults of the making of Arda.

So we can see Tolkien thinking about variant ideas before he finished The Lord of the Rings anyway, more generally speaking. As to the whole tale, this is an interesting question, and there's a very interesting later revision to The Hobbit that might be noted. In the First Edition (1937)...

'... before they came back into the Wide World. In the Wide World the Wood-elves lingered in the twilight before the raising of the Sun and Moon; and afterwards they wandered in the forests that grew beneath the sunrise. They loved best the edges of the woods,...'

This was changed by JRRT in 1966 to read:

'... before some came back into the Wide World. In the Wide World the Wood-elves lingered in the twilight of our Sun and Moon, but loved best the stars; and they wandered in the great forests that grew tall in lands that are now lost. They dwelt most often by the edges of the woods,...'