Hey, Don. Your ABC version is the tune that I know to 15 Men. It's the one that most of our smelly pirate brethern are currently singing.
I first heard it a few years back from Dragonfire, a group in the Miami area. Might it be the tune that Allison and Young put the poem to on their broadsheet?
In any case one should keep in mind that the song was probably not a real sailor or pirate song; a reaction to a passing fad, like modern fascinations with dinosaurs, movie stars, and, errr, pirates.