I thought the Hugill/Lloyd argument was that Haul on the Bowline owes its 'proof' of antiquity to the fact that the bowline became a lighter and less important line - but the song continued (as songs do!)after the time the chorus was directly synchoronous with the task for which it was being used.
Also critical here is Hugill's comment that the OLDEST FORM of the Bowline shanty is in Complaynt. Can anyone quote the form as given there? - bet it's not as we would now know it. All the shanty crews I've heard use the standard Hugill/Lloyd form.
As regard the original question, Bowline is the only shanty for which there is any evidence of that sort of antiquity.