Congratulations on completing your work! While I confess that I did not read your entire paper, I did skim through the better part of it. The statement that caught my attention was this:
The reason this caught my attention is because it is not entirely true.
While Tolkien never directly speaks about myth, stories or Faërie in the book, he does indirectly reference, through the experiences of the characters, what he imagines a good story to be.
In his earlier work, including The Hobbit, Faërie is the name Tolkien used for Eldamar. This is where Frodo, Bilbo, Gandalf, Elrond, and Galadriel set sail to near the end of the novel. So while the term 'Faërie' is not used in The Lord of the Rings, the place itself is referred to, albeit by a different name.
You may also recall that Sam and Frodo discuss the creation of stories during their journey to Mount Doom. (See the chapter 'The Stairs of Cirith Ungol' in The Two Towers.)
'...But I suppose it's often that way. The brave things in the old tales and songs, Mr. Frodo: adventures, as I used to call them...Why, to think of it, we're in the same tale still! It's going on. Don't the great tales never end?'
'No, they never end as tales,' said Frodo. 'But the people in them come, and go when their part's ended.. Our part will end later--or sooner.'
When I think of Tolkien's treatment of the realm of Faërie, I think of The Smith of Wooten Major. The character Smith frequently journeys into Faërie. He finds it wonderful, mysterious, and a bit frightening. It's a wonderful tale, an allegorical tale according to Shippey, and should be read by anyone who enjoys Tolkien.
Faërie is a perilous land, and in it are pitfalls for the unwary and dungeons for the overbold. – J.R.R. Tolkien, ‘On Fairy-Stories’.