Thanks for fixing the "Limber Jack" link, Masato. Lafcadio Hearn must have been quite a guy. In doing a library search on him I came across 500 references, most of which were in the Special Collections section. He wrote about a lot of things.

I am struck by the final "Juba" chorus of his "Limber Jim".

[Patting Juba]
And you can't go yonder,
Limber Jim!
And you can't go yonder,
Limber Jim!
And you can't go-oo-o!

When you compare this to the Fletcher Collins' chorus

Go limber, Jim, you can't go.
Go weave and spin, you can't go,
Buckeye Jim.

the similarities are pretty obvious. Aside from the "Limber Jim" reference, it is the "you can't go(yonder)" that is unique. I have looked and looked for a similar "patting Juba" or a similar phrase and so far have not come up with anything.

The verses in "Limber Jim" (and also "Buckeye Jim") are also unique, though perhaps more closely related to other animal and location songs. I did find a reference that suggested that the "way down yonder..." phrase comes from the ante-bellum minstrel tradition. Also there have been a lot of deaths by "whooping cough" at many "wooden troughs", but not any other old women that I know of. So, I have also been looking through some minstrel and blackface materials, although I haven't been able to get back to any original sources on this.

So, perhaps we have a song with pre-Civil War, minstrel/blackface roots, being reappropriated by Afro-Americans along the Ohio River after the War and being greatly expanded with floater verses and also being given a "patting Juba" dimension. Perhaps this got simplified and somehow found its way into the Appalachians as a banjo tune and became either a children's song, a dance song, or a lullabye, or all three. Obviously we still have a number of missing connections.