Jim,
Excellent info there.
All I have to go on is a hunch and probabilities and possibilities.
You mention other Child ballads in JR's repertoire but they're all relatively well-known and printed on broadsides. Nothing pekuliar there.

Interesting that Edward is described as common in Irish traveller repertoires. I'd certainly be interested in seeing these texts as it is pretty scarce in England and even more scarce in Scotland.