I've finally managed to track down some modern day FAIRBAIRNs of one of my lines, that of Archibald FAIRBAIRN and Elizabeth HOWD/HOUD/HOOD. I've been talking on the phone to a family in Edinburgh, who confirmed that they were indeed descendants of Archibald's son Walter. Now I'll have to finish off a letter to them as they aren't on email. A grddtr in Australia, nephew in Sth Africa, not heard from in many years, son and grdson in Edinburgh, so I've a few extra leads to follow up there.
The FAIRBAIRN descendant chart has been updated with the preliminary findings.