I've also transcribe the related lines from Talley referenced above, though I'm not certain they're related.

Source - T. W. Talley, "Negro Folk Rhymes" (1922), pp. 50-51 (link)

THE OLD HEN CACKLED

De ole hen cackled,
An' stayed down in de bo'n.
She git fat an' sassy,
A-eatin' up de co'n.

De ole hen she cackled,
Git great long yaller laigs.
She swaller down de oats,
But I don't git no aigs.

De ole hen she cackled,
She cackled in de lot,
De nex' time she cackled,
She cackled in de pot.

I fail to see the relation to any of the songs on page 93: link