The only other thing that comes to mind is - When you were looking at the registers, did you make a note of the burials of any Hillsdons before Thomas? I was just thinking that if he relocated to Hillsdon as a child with his family, then the deaths of any Hillsdons in the first half of the 1700s might give you some other names to search for in the hope that you might find a group of baptisms that matched somewhere else.
Very good suggestion, and I got very excited...but I think over nothing...
There were only 4 burials:
22 Nov 1739 Sam HILLSDON son of Tho (son of my Thomas, who married in 1720)
13 Jul 1752 Mary HILLSDON daughter of Thos & Mary
3 Oct 1758 Eliz HILLSDON wife of Thos Snr
5 Sep 1759 Mary HILLSDON daughter of John & Ann
all these burials relate to the same immediate family.
and I have just realized, that the dates that the Bucks FHS have for the burial records are from 1735 - 1901 - so possibly there are no records before 1735? Yet the Baptisms are from 1541 - 1901 and the marriages from 1538 - 1905. Curious.
I shall email the Centre, and see why the burial records only go back that far
