If you are going to eliminate "obscure ballads like Lamkin," you may be shooting yourself in the foot. Probably just about all the old traditional songs from the Southern Appalachians have Scottish roots (except of course the "native American" ones). Bronson did an analysis of a few hundred of those songs by mode and structure, compared them to traditional Scottish and English ones. The American songs differed from the English ones in the same respects as the Scottish ones, only more so. Also, that part of the country was mostly settled by the "Scotch-Irish" and Germans, who came down the hollers from Pennsylvania in the Eighteenth and early Ninteenth centuries. "Barbara Allen" is surely a good example. I'll bet you Sally Ann or Soldier's Joy are also examples.

On the other hand, you are going to find it very tricky to find old Scottish songs of which versions don't also exist in England.