That's very interesting. I am at a loss for James Douglas, gardener in Kilmarnock. He married Janet Sim - daughter of Francis Sim - in 1745. That was registered at Loudoun, Ayrshire. James is named as a gardener on the records available. If he is the same man as the James Douglas born in 1727 to James Douglas (1669-1750) and Jonet Olipher, then he'd have been 18 years old at time of marriage, to a 24 year old woman. Seems possible but perhaps unlikely?
The Clan Douglas Archives aren't sure, but didn't rule out this connection. In any case, we know some of the Jedburgh family did end up in Kilmarnock anyway, which might make it seem more likely that my James was related to them. His daughter Janet Douglas married a man named John Gow, who was soldier in the West Fencibles. Their son James Gow in turn married Christian Reid, and their child Jessie Gow married Andrew McLuckie - from whom I descend.