No explanation seems likely for Wallack's early "Sally Brown," but it is possible that he was simply "chanting" Hood's poem. The Monthly Magazine and British Register for Dec., 1826) says that the poem was known to "everybody" by that that time.

Interestingly enough, the Sally of the poem is just as faithless as the Sally of the shanty. In both the sailor-protagonist sails away and returns to find Sally with somebody else. The similarity could well be a coincidence, but with so little data it's hard to resist grasping at straws. Maybe the shanty arose as a "recomposition," a la Dick Maitland, of the situation in the poem. It's impossible to know, but it would be perfectly consistent with a birth of shantying in the 1820s and '30s.

I agree that there must have been a "historical moment," but that "moment" could have been some years in duration. It isn't enough to have one crew of oddballs singing call-and-response at a job : that might have happened at any time after ships got big enough. The "moment" had to begin when a small repertoire of shanties - even just one or two - had become so familiar that an influential number of crews (maybe inspired by a single crew of innovators whose habit of shantying gained some "folk notoriety" in one or more ports) were using them. The "moment" would have ended (probably by 1850) when shantying was a well established practice.

A number of factors must have come together to create that innovative "moment": the adoption of stowers' chants, the desirability of adopting them, advances in ship design, more demanding schedules, more sailors, maybe even more citizens coming down to the wharves to watch vessels heaving anchor. That by itself might have done wonders for the capstan shanty especially. (In fact, maybe singing at the capstan - any old song - may have been the model for singing more specialized songs while hauling.

The more primitive-form bunt shanty like "Paddy Doyle" might also have been early: "Paddy" is hardly more than a creative elaboration of a spontaneous chant like "To me one! two! three! four! Get ready you sailors to PULL!" As I've said before, few writers would have found something so simple to be worth writing down. The level of atmospheric, documentary detail expected in popular fiction and nonfiction today is vastly greater than it was even a hundred years ago.