Well detected, Mike!

Had a good look at all of the broadsides I have and they are (not as I wrongly remembered) closely related. None of them are 17thc. The earliest and longest which looks like it may be the original c1750 has 41 verses but contains all of the verses in the later broadsides some almost verbatim and a couple paraphrased. This is 'The Fortunate Sailors Garland' printed by L. How of London. The 3 later broadsides of about the turn of the century are very likely oral versions of a shortened version of the How version, or possibly 2 derived from one of the others. None of the other 3 have more than 9 verses but 2 of them have interesting choruses which relate to later oral versions.

The later titles are :
The Jolly Jack Tar printed by Catnach of London and Williams of Portsea stanzas ABCDEFGHI and chorus
The Merchant's Courtship to the Brazier's Daughter, printed by Evans of London and Pitts of London, stanzas ABCDEFGHJ and chorus.
The Sailor's Frolic, pr by Moore of Belfast, stanzas BCADGHIF

The Moore printing looks to be an oral hotchpotch of the Catnach/Williams version.

More when I've been through all of the oral versions I have.