I don't have much of an opinion on this, but one point that's noteworthy is that Child 239 has a very unusual stanza pattern. (This isn't my observation; it's William Bernard McCarthy's.) Standard ballad meter is 4343 rhymed xaxa. Child 239 is 4444 rhymed aabb.

Is there another tune that scans 4444 and rhymes aabb? It might be that all these sources are remembering and borrowing from that tune.