Jack,
What is the main source of this tune that starts high and descends? I only know it from the singing of Ian Manuel but I think it comes ultimately from the Scottish travellers, Jeannie Robertson perhaps. I seem to remember Isobel Sutherland also sang it. For what it's worth, and I'm no expert on tunes and their origins, I think it is very uncharacteristic of ballads and if pushed would guess it had some sort of artistic origin in the 18th century. The few versions of the tune I've just looked at from Scottish sources (Greig-Duncan, Christie) don't appear to bear any resemblance and start low.

As I've already said, I love the tune and think it fits the text beautifully despite the lack of minor key.

As a little experiment I tried diddling it in jig time and it sounded remarkably like George Morris's The Moss o' Burreldale, Not the 'Tinker's Wadding' one. Perhaps that's where Morris got it from.