(Some of this has been posted, but a summary will help my old brain keep these songs straight).

"Last Gold Dollar," Bascom Lamar Lunsford, from the album "If You Ain't Got the Do-Re-Mi," Smithsonian Folkways, mp3 can be downloaded at Amazon.com for $0.99.

"My Last Gold Dollar," two versions, are in Vance Randolph, Ozark Folksongs, vol. 4, pp. 114-115, with brief musical score. He notes that it also appeared as "My Last Ole Dollar" which are printed in Spaeth and Lomax (FSNA).
The Traditional Ballad Index lists the song under "My Last Gold Dollar, " with the "Ole" or "Old" listed as a variant. McClintock used "Old."
The 'gold' refers to gold-backed paper money, issued during the Civil War, and, I believe, in circulation for some time after. "Old" is more understandable nowadays.

"Mole in the Ground" is a floating verse which appears in some versions of "Last Gold Dollar."
As a song "Mole in the Ground," Lunsford recorded it in 1924, but it had appeared in collections before then, e. g. Brown, North Carolina Folklore, vol. 3, no. 173, prints a six-verse version of "Mole in the Ground" sung in 1921 by Fred Moody (has Tempy verses).

Lunsford is usually credited with "Old Mountian Dew." In earlier posts, I have referred to earlier 'Mountain Dew' songs, but Lunsford's seems to be unique.
The Harrigan song hasn't been posted, but I doubt that Lunsford knew of it or that there were folk versions.