We have spoken before about our family links (BRUCE etc), but I have only just come across this post of yours about ORCHISON. It is an very unusual surname, and it also crops up in my research...
I believe that George BRUCE b1783 Airlie (1st son of George BRUCE/BRUICE and Elizabeth GEORGE of Airlie [who you know of]) married Jean ORCHISON in Edinburgh 1804 and had 4 children.
And that he later married Elizabeth DAVIDSON in Dundee and had another 4 or 5 children.
Your William may be a brother or cousin of Jean???