Here is a bit more of Gardner-Medwin's argument for earlier, Scottish influence on the "House Carpenter" tradition in America. A question that arises out of her comments would be how did these Scottish-influenced traditions move from the Southern Appalachians north into the New England region? I think we are always assuming that everything was moving south and west and never the other direction. But surely that can't be accurate.

""The internal evidence from the words of the American versions of Child 243, which we have been examining, seems to point to a very strong Scottish influence. There is also a certain amount of evidence that the ballad was current in America some considerable time before it emerged in print in 1858. How far back can we reasonably make it? On the evidence furnished by the words themselves we can only say that there must have been several streams of influence from Scotland, and it is probable that the song had been in oral tradition in America for several generations of singers before the end of the nineteenth century."
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"Ian Charles Cargill Graham shows that between 1707 and the American Revolution merchants of the port of Glasgow made themselves the chief traders of tobacco between Virginia and Europe.[30] As well as carrying tobacco these merchants established stores in the Fall Line towns of Virginia that became centers of trade and, I suggest, also of cultural exchange.[31] Moreover, although the factors themselves went back to Scotland at the time of the Revolution, there were settlers who stayed."
....
"Therefore, it seems reasonable to suppose that ballads from Lowland Scotland could have come to the Southern Appalachian area by one of two routes, either directly from Glasgow in the eighteenth century or via Pennsylvania after a stay of a generation or two in Ireland. With regard to the particular song under discussion it, was published as a broadside (Child B ) too late (1757) for it to have come via Ireland so it seems probable that this was a song that traveled to America with the Scottish tobacco traders."
....
"I am inclined to think that the Scottish element in the ancestry of "The House-Carpenter" is rather stronger than the English, and that the ballad must have migrated to America in several versions (the Scottish versions differ appreciably among themselves as well as from Child B) which have inter-related among themselves in America between 1775 and the present day. "
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"I believe that the ballad known in Scotland as "The Demon Lover" and in America as "The House-Carpenter" came to the Southern Appalachian region from Scotland in the middle of the eighteenth century. There it was current in oral tradition, being changed in small details, such as the name" Tennessee" which reflects the local geography as known at an early date, and surviving until the twentieth century as a living entity. It gathered up elements, at times from other ballads, and in its turn influenced them. It was picked up in the mid-nineteenth century and printed at least twice( 1858 and 1860), and these printed versions combined with the oral tradition to reinforce some of the changes."