How good to hear from you. I am pretty certain that we are related. My Jane Aitchison was born in Wilsontown in 1837. She did have a brother George born in Wilsontown in 1835 but, unfortunately, he married a Christina Goold (also born in Wilsontown)and not Rebecca Nielson.
My Jane Aitchison's father was John Aitchison born in Wilsontown about 1812 who married Janet Campbell. I think that your George Aitchison (who married Rebecca) might be the son of a brother of John's.
The parents of my John Aitchison (ie Jane's grandparents) were John Aitchison and Jane Forsyth. Do you know the name of the father (and, better still, the grandparents) of your George Aitchison?