I'm not sure we're not talking about two different songs (i.e., Jimmy Crack Corn & Blue Tail Fly) that, since they share the same, or similar tune have been confused by cross-over versing. My grandfather, who was born (1885)and raised on the mainland behind Pawley's Island, South Carolina, sang 'Jimmy Crack Corn' at every family gathering through the 1950's. The version he sang was very similar to Ruth C. Seeger's animal version. He said he learned the song from the local 'Darkies' when he was a kid. He must have known twenty or so verses and never included any of the Blue Tail Fly verses. Of the ones he use to sing, I only remember the following two:

Down in the foul house, on my knees
A'listenin' to those poulets sneese
Duck chaw tobacco and the goose drink wine
Tha Turkey danced a jig on tha sweet potato vine

(coda)

So said the bull frog to the crane
I wish that the Lord would send some rain
The creek's all muddy and the ponds all dry
If it wasn't for the tadpools, we'd all die

(coda)

Other that saying where he learned, he never speculated on it's origins.