Thanks, Brian, for supporting my suspicion that there are some sources other than the DeMarsan broadside feeding into the North American development of this ballad. I suspect that this ballad was alive and well and came over with at least some of the Scotch-Irish immigrants themselves.
I don't know much about the whole business of the Broadsides and would welcome some education on that. Do we know how many copies they would print up and would they do reruns? How many copies of the DeMarsan printing could we reasonably expect to have existed? They would have been disseminated from New York City. I assume that was a major entry point for the Scotch-Irish. Treading very lightly, I wonder how literate these folks were when they arrived. And what about the tune, which seems fairly stable? Also, what about that earlier (?) version printed in Philadelphia? Do we have textual evidence of that somewhere? Philadelphia would certainly have been a major port of entry for the Scotch-Irish.
According to the Wikipedia article, by 1775, there were already over 200,000 Scotch-Irish immigrants in this country scattered from Maine to Georgia. They had been arriving since 1710. This is well before the printing of the DeMarsan broadside. How likely is it that this printed song sheet found its way into the Southern Highlands? Or the hills of Kentucky and West Virginia? Or the lumber camps of Vermont and Maine? Another 100,000 Scotch-Irish immigrants arrived by 1812. Again, some forty years or so before DeMarsan's printing. Is it not likely that his version of this ballad was actually taken from these immigrants at some point, after they had become relatively well established in North America? This second "wave" was apparently somewhat older in age, and perhaps more skilled and tended to settle in the industrial centers of the North, like New York and Philadelphia. But were they the ballad singers? Weren't the "ballad singers" already several generations established in the Appalachians by then.
Another half a million arrived between 1815 and 1845. They just kept coming! And they spread out across the developing new country. And somehow they took this ballad with them. I suspect that whether or not they first received this ballad in printed form, many of them did in fact write it down for themselves and preserved it in that way as well as in their memories. The tradition of the "ballad boxes" surely plays a major role is stabilizing these texts.
This is all fascinating to me. I just wish we had more printed references to work with on this.