I've looked for "I Get In A Weaving Way" without success in a number of collections (Oxford OLIS, Australian Nat Lib, Californian Sheet Music Project, Duke, Plymouth Library Services, Southern Folklife at UNC and a few others).
I did find the following reference to the Happy Miner at Utah State in a collection of songs collected by anthropology students as part of their studies. This might suggest there is a tune there: Fife Folklore Archives - Group 5 - Songs