I have mentioned this in a more recent related but different thread, but here it is again, to close this thread.
I last week contacted my 3rd and 4th best matches on GEDmatch. To cut a long story short, they are both descendants of an extended family living in Tudhoe, probable birthplace of my great grandmother, Jane Adamson. We can't be sure who in the family was actually Jane's father, but it leaves me in no doubt that I have Tudhoe connections in about 1860, my grandmother, Jane Adamson almost definitely came from there, and I consider this and earlier research to meet the proof stanards. Thanks to all.
Martin