That does make it a little more difficult too doesn't it!?
Another thing that I am mindful of, is that Patrick had a son named Anderson & this name was carried down through quite a few generations.
From the way my tree is panning out, I would be surprised if the name 'Anderson' didn't appear in Patricks generation or possibly his fathers generation.
Other than 'Scotlands people', 'Free Reg', 'Family Trees', and 'Ancestry.com' - could you possibly any other sites that i might be able to try?