Thanks for digging this out, Carter! It's very enlightening.

Here's a current banjo performance of "Cackling Hen":

https://www.youtube.com/watch?v=BFRcld549pA

I first heard the tune when I was trying to learn old-time banjo 50 years ago. At that time I could already play "Cluck, Old Hen," and the tunes seemed quite different. Now I hear a slight similarity only, at least in the Gibson-Hicks version. IIRC - and maybe I don't - the "Cackling Hen" tune was played in ordinary G tuning. I never tried to learn it.

Aside from minstrel material, names of banjo tunes before the "hillbilly era" are even harder to find than fiddle-tune titles. And there are no nineteenth-century tune transcriptions - again except for the minstrels.

I find several refs. to “Old Hen Cackled” from around 1900, which suggests that a tune by that name was already widely distributed in the South and was assumed to be old:

St. Louis Post-Dispatch (March 5, 1899), p. 25: “ ‘BLACKVILLE’ BALL AT LITTLE ROCK, ARK. …He will open this grand affair with one of those old reel dances of the year 1700, entitled:

                           The old hen cackled,
                           But the rooster laid an egg!”

“The Old Hen Cackled” is mentioned in the Marion (Ala.) standard (July 5, 1900) as an “old-time tune,” and the Sequachee (Tenn.) Valley News (Apr. 15, 1909) quotes a whole stanza as a throwaway one-liner:

“The old hen cackled, and she cackled in the lot, but the next time she cackled she cackled in the pot.”

In Jounal of American Folklore (1913), E. C. Perrow printed a text with the "...rooster laid an egg" business as a refrain. His source had learned it from "Mississippi negroes" in 1909.