The original framing story for Tolkien's Book of Lost Tales, which later developed into The Silmarillion, was a sailor named Eriol/Ælfwine who chanced upon Tol Eressëa and was told the stories by his hosts in the Cottage of Lost Play.
By the time the Lord of the Rings was published in 1954, the in-story source had become Bilbo's Translations from the Elvish, part of the Red Book.
In a comment on this question about the Notion Club Papers, @DavidRoberts expressed his doubt about whether the framing had changed by the time NCP was written in the 1940's. I was pretty confident it had changed by then, but when I dove back in to the HoME books I became less sure. Thus this question.
A draft of Book I of LoTR (appearing in HoME VI, Return of the Shadow) was completed by the time in question. In August of 1939, there appears to be a version of "A Long-Expected Party" where Bilbo talks about taking his "Book" with him to Rivendell. But this book probably only consists of There and Back Again -- the Translations are framed to have been written by Bilbo while living in Rivendell, translating Rúmil and Pengoloð from Elrond's library.
The initial drafts of the chapter that became "Many Meetings" (later to be moved to Book II) don't mention Bilbo at all, and it's Trotter (still a hobbit) who relates the story of Gil-Galad to Bingo and the other hobbits.
After writing these drafts, (which failed to reach the Council of Elrond), Tolkien got stuck, and went back to rewrite the whole thing.
Tolkien started writing the "Later Quenta" that appears in Morgoth's Ring around 1950-1951, after LoTR was essentially complete, so by this time, Bilbo seems to have supplanted Eriol/Ælfwine.
I'd like to know if we can pin down exactly when Bilbo's Translations got into the text.