Cranky, your version is closer to the one we sang as kids (yowling at the moon) back in the 30s than the one in the DT. The last verse in DT seems to be a late add-on.
It is earlier than the Lomax 1911 date. The Traditional Ballad Index (Fresno) has dates going back to 1876, better evidence for the 80s and definite for 1904 (as Arizona Home).
That it was sung to Franklin Roosevelt by newspaper reporters when he was elected (see DT) is probable; it was certainly sung by drunken reporters (and other drunks) to almost everyone on many occasions from 1920 on, if not earlier, yowled to girl friends by young men passing puberty and sung in every bathroom in the country.
Another old curmudgeon.