Unprovable hypothesis alert.

John Masefield was confident that "Haul on the bowline" must go back to the 16th C. because the bowline, by the 19th, was no longer a rope that needed a shanty. Other writers have rightly criticized Masefield for his assumption. However...

It does seem unlikely that a shanty would arise telling the crew specifically to "Haul on the bowline" (and only the bowline) at a time when the labor would be unecessary. Sure, it could have started as a joke, but here's another theory.

Maybe the shanty developed from a "bowline singout" that really does go back centuries. Consider the tune of the words: "Haul on the bowline" - three close notes for five syllables. If the final syllable of "bowline" is shouted higher rather than sung lower, it becomes indistinguishable from a singout. The shanty may have developed from a repetitive singout: "Haul on the bowline!" (They haul.) "Haul on the bowline!" (They haul.)

Then one day, the proto-shantyman gets tired of "Haul on the bowline!" and follows it up with a second, more tuneful "verse," "So early in the morning!" Later, maybe years later, some crew adapts the first verse as a chorus. Ad lib to suit and voila! a shanty (maybe the earliest indeed).

No early writer would have noticed, because there's nothing interesting about sailors hauling on a bowline while someone yells, "Haul on the bowline!"

Just speculating.