The Lord of the Rings involves a literary conceit that Tolkien has received the story (and perhaps more) as an actual history, translated from The Red Book of Westmarch. Given that Tolkien's world-building of breath-taking depth is centered strongly on philology and constructed languages and the histories they imply, I wonder:
Did Tolkien write any significant part or passages (e.g., songs or poems) of the history in either The Lord of the Rings or The Red Book of Westmarch? (Note: I am not asking if he wrote and then translated from Westron, but simply if he ever wrote any passages or even large parts of the narrative in Westron, presumably after the fact of having written LotR.)
My sense from his published fiction, essays and the very few of his letters I have read (I have not read The History of Middle Earth) is that Westron is maybe less developed than his Elvish languages, so I expect the answer to my question to be in the negative.