After a bit more searching I believe it was the Oliver Ditson version called also "Jim Crack Corn" that Lincoln liked. I say this because the Virginia Minstrels played for him and that's the version they sang. Where my man fits into all this -- I still just don't know exactly. He associated with The Virginia Minstrels about the time of their formation.
Neither version has an author -- unusual at this time. Could it be that my man wrote the Benteen version? He always claimed the song "The Blue-tail Fly as "his song". Did the Virginia Minstrels add a chorus and change the tune? Are both versions written by the same author who abandoned one of them to make the other his performance piece?
Anyway here I go. A considered opinion:
I believe minstrel - Robert "Billy" Barlow (aka The Inimitable Barlow, American Barlow, Australian Barlow, The Inimitable Mr Barlow)
wrote the song "De Blue Tail Fly". The one published by Oliver Ditson in 1846.

Cheers, Joy