Geordie told me (years ago) he got the melody from Andrew Tannahill who was a great-great grandson of Robert Tannahill. He said that Andrew Tannahill chanted the tune to him, ".... if you can class a half spoken rendition as a chant. I've been singing it for so long it may be be that I have modified it".
I think therefor that his melody owes much to his inventiveness rather than tradition. I agree, however, it is a beautiful version they sing.