Leenia: The Traditional Ballad Index is a work in progress. By searching in Google Books, I have found several examples of published songs that are older than the "earliest date" posted at TBI. When I notified the editors of the TBI, I always received a personal note of thanks.

If you can document the fact that GOING TO LEAVE OLD TEXAS was published earlier than 1966, I'm sure they would like to know about it—but I doubt that they would accept your memory of yellowed song sheets as sufficient evidence.

It was sufficient to make me go looking in Google Books, however. When I search for the phrase "I'm going to leave old Texas now" (in quotes) I find that that phrase appears in Cowboy Songs and Other Frontier Ballads by John A. Lomax, Alan Lomax, and Edward N. Waters. (New York: The Macmillan Company, 1938).

But that edition is not viewable online, and earlier editions apparently don't contain the phrase. Without actually seeing the book, I can't tell whether the whole song is present, or it's merely mentioned in a footnote.

So I'd say that's pretty good evidence that the song was at least known, if not fully published, in 1938.