I read that Tolkien didn't want to make the Lord of the Rings three books, and that the only
"natural divisions are the 'books' I-VI (which originally had titles)"
What are those titles?
Footnote 1 of the "Note on the Text" in the 1987 edition (and later editions?) of The Fellowship of the Ring:
Tolkien's titles for the six books were not used. A contents listing with the manuscript of The Lord of the Rings at Marquette University gives them as follows: Volume I, "The First Journey" and "The Journey of the Nine Companions"; Volume II, "The Treason of Isengard" and "The Journey of the Ringbearers"; Volume III, "The War of the Ring" and "The End of the Third Age." A variant set of titles can be found in Letters of J.R.R. Tolkien, p. 167.