Malcolm, I consulted ProQuest's American Periodicals Series 1740-1900 Online, available to me through my university library.

This is a great resource in general, but the pickings are slim for traditional songs - perhaps even surprisingly so.

Meself, it seems likely that Ludlow heard the song from a singer much like the one he describes. If "our grandfathers" refers to thirty rather than fifty years earlier, it would fit nicely with the "1829-34" date assigned to the Boston broadside. Even in those days, a song sung in Boston could have made its way to New York State rather quickly.