Also from the early 30s is this reference:

"Waldie's Select Circulating Library," II (Dec.
24,1833), p. 581:

"The pirates pulled merrily for their schooner, singing in chorus the
well known West Indian canoe song:

"The captain's gone ashore;
The mate has got the key;
Hurrah! my jolly boys,-
'Tis grog time o' day!"

This "Grog Time of Day" is the song sung by the Jamaican stevedores in 1811. John M. has just demonstrated an instance of the same work-song being used for both rowing and corn-shucking. Here, there is something important, I think: a song being used for rowing and also for loading cargo. The next step in the "chain" may have been using such a song aboard ships.

In the 1811 Jamaica case, the capstan in vaguely alluded to. However, I am unclear why the stevedores would be using a capstan to load cargo. I can imagine it working, but, unless it was extremely heavy, that would seem less efficient than hauling the cargo to a height, in halyards fashion. In point of fact, another reference I've seen (it may come later) talks about loading in this hauling/hoisting fashion. And, even better, Lydia Parrish has a photo of chantey-singing stevedores from her Georgia Sea Islands community performing such an action, just as one would haul halyards on a ship.

It would be "nice" to imagine the 1811 stevedores were also doing that when singing "Grog Time", as it would establish a firmer link between the idea of a rowing action and a halyard-hauling action. However, I'm not sure that can be established. If the stevedores were singing "Grog Time" at the capstan, then it would not indicate any necessary or special "timed action" section to the song that helped it to jump from one similar task to another. No, it would just be a song, perhaps especially associated with work among West Indians, and with a steady rhythm to be sure, but not necessarilly bound to specific jobs. Of course, as has been noted, a song with special "timed points" is nonetheless easily adapted to capstan, regardless.