Today I managed to extend the Roberton branch another generation. Using IGI records, I found that the earliest Thomas Roberton I had was born on 7th February 1776 in Linton, Roxburghshire, Scotland, and that his parents are yet another Thomas Roberton and Katherine Hogg.
That still keeps us in the eighteenth century but it's a different part of Scotland. I wonder if I can fill out any more details about his life.