good to hear from you again. Like you, I only have proof back as far as James Turton and Susanah Askham (his second wife, Jane Tops being his first).
I believe that his parents may have been Edward and Elizabeth Turton. They appear to have been the only Turton family in Tydd St Giles at the time but I have yet to find a reference to his baptism (one originally showed up in the FindMyPast database but has subsequently been removed).
I'll let you know if I come across any further information.