Delos, Is it possible that there is a wrong connection when you say "the William born in 1779 is claerly the William who married Martha Burnill in 1802"? I believe that the William who married Martha Burnill was William Hepworth, born 1782 son of Robert Farnill and Salena Hepworth married in 1781. I suspect that Robert Farnill was the Robert Farnill christened in 1751 at Fewston. Son of Thomas Farnill and Elenor Carr married 26/1/1751.
I have also found a Thomas Farnill born 1713 at Nidd Yorkshire who would be the right age to have married Elenor Carr.
There was a Robert Farnill born 1669 who married Mary Slater in 1701 and could be Thomas's father.
These are mainly guesses based upon names, dates and places, Can you shed any light ?