I don't know too much about the Griffiths Valuations except it gives the names of leaseholders, who you would expect to be the the head of the house. Seeing a woman named, I assumed the lease would have been passed to a widow from a deceased husband. I can't imagine that a young single woman would be a lease holder. That is why I speculated that "Sarah Fullerton" might be the widow of James the schoolmaster.
Regarding the posted death certs - the images posted are too small to read on the screen, and I think it might be a copyright infringement to post the whole thing anyway. It is always a good idea to look at who the informant was, to see how accurate their knowledge and recording of details might be.
I believe there’s doubt that your hypothesis is correct regarding Sarah.
I have achieved my initial request in finding out who was the mother of John and much much more and everything else is a bonus.
I have collated most of this thread on my tree on Ancestry!!
As you will be well aware “facts” can change!!!!
Thanks again for your time and effort.
Cheers Tam