Gibb-

Well argued as usual!

"Heave away, you rolling king" may simply be a description of what the stevedore was doing while shifting a bale of cotton along the dock or up the gangplank of a ship.

One gets a similar sense of what the stevedores were doing from this verse from a minstrel song from the 1850's:

As sung by J. Smith of White's Serenaders at the Melodeon, New York City, from White's New Ethiopian Song Book, published by T.B. Peterson & Bros., Philadelphia, US, © 1854, p. 71,

Storm Along Stormy

O I wish I was in Mobile bay,
Storm along, Stormy.
Screwing cotton all de day,
Storm along, Stormy.
O you rollers storm along,
Storm along, Stormy.
Hoist away an' sing dis song,
Storm along, Stormy.

And, of course, this may be our first encounter with "Stormy" as well.

Cheerily,
Charley Noble