I don't want to rain on your parade, but Cordiner is an occupational surname like Taylor, Mason, Fisher, Baker/Baxter and so on, and Sophia was by no means an unusual name in the fishing ports. In my native East Neuk of Fife the women in the fishing communities weren't all Jessies and Jeanies, they might be called Sophia, Rachel, Amelia, Penelope, Charlotte, all kinds of names we might now consider "posh". There was nothing posh about Penelope Barclay in my native Cellardyke who one night when she was drunk threw a dinner plate at her husband Alexander Smith, severing an artery in his temple and nearly killing him. She was tried at Cupar sheriff court and sentenced to several weeks in jail.
Harry