The declining run in the B Section cannot be earlier than Mozart, for starters. It might be argued that it's post-Corelli in the O'Carolan descent, but even that is a bit early for the US - go listen to Joel Cohen's work, for example The Liberty Tree, to get a sense of the relative seriousness of American music in the late 18th Century. Was it true of the Appalachians? Hard to tell.
Another distinctive decoration is the triplets in the A part, which are not found before Chopin c1838: before that, these were treated as rubato.
So putting the tale-telling together with the evidence and we come to a dat fairly close to 1840. QED.