In the version of "Wedderburn" with which I am familiar (sung by Ewan McColl), there is no mention of Melchizedek.   The answering reference to "a priest unborn" is that

"The priest is standing at the door
Just ready to come in
No one can say that he was born
No one unless he sin
A wound cut in his mother's side
And he out o't did fall
And we'll baith lie in ae bed
And You'll lie niest the wall!"

It's possible this is no news to anyone, but I can't tell from previous posts whether this is widely familiiar.

Dave Oesterreich