Jon,
The tune in Greig Duncan looks to me to be closer to the older song but somewhere in between the 2. Would it be a help if I scan it and send you a copy?

FWIW Greig in FSNE article 176 gives GD versions B and C but declines to print the rude v4 in B.

Karl Dallas in 'The Cruel Wars' gives Jeannie's version with vv3&4 interchanged with tune as does Norman Buchan in 101 Scottish Songs p76
and Alasdair Clayre in 100 Folk Songs and New Songs all derived from Jeannie.