Steve, the author speaks generally about "chanteys" - which he uses to mean any sea songs sung by old sailors, then speaks briefly about songs known to "Pop" McKinney, whom he had met in 1917, and who had gone to sea not long after the Civil War ("fifty years ago").

Besides "Off to Sea Once More," Swift gives a stanza and the chorus of "Mainsail Haul," which I posted to that thread ("Valparaiso/Paddy Lay Back") on Aug. 30.

He also gives a text of "Leave Her, Johnny":

"The times are hard and the wages low,
   Leave her, Johnny, leave her.
The times are hard and the wages low,
   And now it’s time to leave her.

Since the day we sailed from Birkenhead,
They whacked us out of a pound of bread.
Our work was hard and the voyage was long,
The seas were high and the gales were strong.
The food was bad and the wages low,
But now ashore again we’ll go.
The sails are furled and our work is done,
And now on shore we’ll have our fun."

Most of these lines are familiar, showing that chanteying was not all improvisation all the time. (I suspect "of" in line 2 is an error: "whacked out a pound" means "gave a pound out.")

Swift also gives part of what's pretty clearly a stage song, "The Jolly Tar":

"When a man of war or merchant ship comes sailing into port,
The jolly tars with joy sing 'a land, ahoy!' [sic]
For there's money in their pockets and a parrot in their cage,
And a smile for all the pretty girls upon the landing stage.

                      CHORUS

Away, hawl away. Oh, hawl together, oh!
Away, hawl away - oh hawl, hawl together, Jo!


Swift also mentions that McKinney knew "Reuben Ranzo," but regrettably doesn't quote it.