The Roud Index has The Happy Miner as #4351. As well as Lomax's Cowboy Songs (1919, 1934, 1938) he gives 2 entries under the title of Gatineau Girls collected in Quebec by Edith Fowke and published in Lumbering Songs from the Northern Woods and 2 entries under the title The Jolly Shanty Boy published by Earl Clifton Beck in They Knew Paul Bunyan and Songs of the Michigan Lumberjacks(1941).
Without seeing the tunes, it's hard to tell if these others use the same tune as The Happy Miner, but if anyone has access to them it might be worth a look. There are references to both of these songs on the web, but I haven't time to follow them up just now.