Julia, by "the tunes you speak of," do you mean the three I named or "Appalachian fiddle tunes" generally?

It would be nice to see specific examples of American/Appalchian fiddle tunes that are the same as or clearly derive from Transatlantic sources.

Obviously the American tunes didn't just appear from nowhere. The reel and hornpipe forms were clearly brought from Britain along with the modes. Undoubtedly the Colonists brought their music with them, but that was over two hundred years ago. Those early tunes seem to have fallen out of tradition long ago.

Consider the Irish immigration of the 1840s. Many tunes of that era survive in Irish-American tradition (with occasional booster shots from print), but except for "The Red-Haired Boy," which is known to old-time American fiddlers, I can't think of any that spread beyond Irish-American communities.

My position at the moment is that while there was strong stylistic influence from Britain and Ireland, the vast majority of American fiddle tunes were home-grown - with some new (or newly widespread) stylistic developments as well.