It's probably off-topic as far as the Carpenter versions are concerned, but the history of this ballad interests me a lot. There's the early 'Miller and the King's Daughter' reproduced above, which looks like a burlesque, and similar though not identical burlesque versions from the 19th century under Child 10L. Aside from those, all of the variants from England that I know of are of the 'Bow Down' type, with no supernatural element.

The Appalachian variants are likewise the 'Bow Down' type, apart from a couple of rogue versions with 'Wind and Rain' or 'Jenny Flower Gentle' refrains, which are the only US versions with a magical fiddle or harp.

Then there are various Scots examples, mostly including magical instruments, ranging from the 'Bows of London' and 'Swan Swims so Bonny' refrains, to all of the 'Binnorie' / 'Edinboro' variants which Bronson seemed to think were derived from Scott's 'Minstrelsie'. 'Binnorie' is vanishingly rare in the US.

So my question is, what's the oldest example of the 'Bow Down' type? Its currency in Appalachia would suggest that it was around in Britain by the mid-18th century, but it's very different from 'The Miller and the King's Daughter'.