Hi Dave,
I've just been reading through this thread with interest. While I can't add anything to your immediate question, I can add something about Charles' parents.
Over the years, I have collected bits of information here and there on the Pyne/Pine name as a sort of one name study, given the surname's common Devon origins.
I have in my notes Charles as the son of William and Prudence, as suggested above. However, it has probably been taken as face value from records. Where possible I have tried to draw up family units.
One suggestion if you haven't considered it, take into consideration the name might be spelt as "Pine" instead of "Pyne". The two are virtually interchangeable. Even in my own line, Pine becomes Pyne a few generations back, simply by moving towns.
There was quite a family of Pyne's/Pine's in Exeter who were fullers and similar trades.
Hope this helps.
Darren