Hello Tim,
Alexander emailed me to say you have this thread on Rootschat. Thomas Pitchfork and Mary Chauntry are my 4x gt. grandparents. I have been researching the Pitchfork family on and off since 1988. Whilst I can't hold out much information about Elizabeth baptised 1793 and her parentage I can tell you about the family in general.
Thomas Pitchfork was, I believe, the son of Peter Pitchfork and his wife Mary Hees who married at Warsop in 1756 but as you have noted there is another family from Soulkholm with a son named Thomas. William and Mary Pitchfork (I don't have a marriage for them); their descendants go into the area around Grindley-on-the-Hill, Nottinghamshire and into Lincolnshire near Gainsborough. Each family also have a daughter named Ann but that is a complication we don't have to consider right now.
I will send you family group sheets for Thomas and his two wives Mary Parsons and Mary Chauntry via the PM link when I can work out how to use it - haven't been on this site for a long while. As soon as I can I will have another look at the parish registers relevant to the family to see if I can find anything further.
Best wishes,
Janeada