"Can anyone think of a reason why any of these shanties would not have been current then in that location?"

Unfortunately I can: there is no documentation that they were. And   the researcher always bears the responisibility of establishing the reliability of the evidence before he goes on to discuss it or apply it.

As far as I can tell (and you may know more avout it than I do), any statement about particular shanties (and perhaps even shantying in general) in the period before Dana and "Steerage Passenger" is based entirely on inference, supposition, informed guesses, etc.

While it seems extremely likely, for reasons we know, that many or most of the well-known "revival" shanties - at least their tunes, choruses, and some of the familiar verses - were sung in the 1850s and earlier, we can't apply that very general statement to any particular shanties without particular documentation.

Words that might come in handy in a discussion of early shantying include "possibly," "plausibly," "conceivably," "presumably,"
"likely," and "uncertain," "unclear," and "maybe."