I have just found the following and wonder if it ties in with anything you have.
John ALCHERSON m. Katharen SUTHERLAND (banns at Brabster 21.3.1747 Their son, James, b. Larel 19 10 1747 m. Marjory RYRIE in Bower, Caithness Their son, John b. Bower 12 1 1779 bears the surname ALEXANDER.
The following is an excerpt from the letter which accompanied the tree:
"The attached tree is the best that research has produced so far and altho' to be treated with some reservation, is likely for several reasons.
1 There are no records of the name ALEXANDER in Caithness and similarly no ALCHERSONS, ALCHERS or ALSHERS in the London telephone directory, but in view of the obvious drift southward of many Scots the researcher's theory that they changed their gaelic or Norse surnames to anglicise themselves seems a reasonable assumption.According to LACK and other authorities ALEXANDER was often used."