I would be interested in seeing any evidence for your assertion that the screwing was done at the end of a verse/chorus.

The condensed argument is at the end of the "Screwing Cotton by the Day" paper.

We don't have recordings of cotton screwers so we have to reason by comparing various evidence that we think likely to be relevant.

For evidence that I think is relevant, you can start with this performance of Georgia stevedores. The exertion comes following the chorus, causing the length of the song to be extended, and the regular meter is accordingly disrupted.

"Pay Me" led by Joe Armstrong

See also menhaden fishermen's chanteys, i.e.

https://youtu.be/geAJI6he75I

While these don't say how cotton screwing was performed, they indicate that there existed a method of working to chanties, by Black maritime laborers, wherein one "works" after the chorus.

Can add more later...