Katie Lee said, p. 219, with the verse with chords I reproduced above: "The melody used here might be the work of a professional songwriter like Bob Nolan of the Sons of the Pioneers. Whoever "re-tuned it from the earlier, simpler, one made it stick, because it's not heard to the old melody any more."
In other words, it can't be credited definitely to anyone without further investigation. Perhaps I should have written 'not known for certain' but anon. is not too far a stretch at the moment.

The version may be the one sung by Bing Crosby in "Rhythm on the Range," 1936. Also recorded by Crosby with Victor Young's Orch., on the Decca lp "Pennies from Heaven." It may have appeared on a single in the 1930's. His "Tamma-- sounds a lot like ta-hum a la de day. The cut was released again in 2000 on "Bing Crosby Going Hollywood Vol. 2, 1936-1939;" the clip I found is too short to evaluate the music.

If Clark did OK the Ross version, he was probably either drunk or starving.

The 1919 Philleo in the Colorado collection probably is a reprint; the song was copyright 1917.