I've always thought of Mole in the Ground as a play party song, and Lunsford's version -- the "standard" one I learned years ago -- as one rendition but not canonical. When I play the tune for elementary school groups, we do it as a game where I do the mole verse and then they take turns naming animals and I make up verses to go with their selections. I figure that's perhaps where the verses in Lunsford's version originated, and that's why the sequence doesn't seem to make much sense.

By the way, the kids always pick tyranosaurus rex as one of their animals.