Hi Paul33,
This is getting a bit confusing! You have 'wandered' over into the Blewbury Blissetts in my tree but we appear to differ about 'your' John's origins. It doesn't help that this area seems to be the dead centre of the world's Blissetts!!
I don't have access to the PRs for Sutton Courtenay nor can I find it on Family Search so am in no position to query your baptism date for your John Blissett but I think you may have missed out a generation - or I've got it wrong, which is quite possible!
Probably best if I just tell you what I've got and leave you to make of it what you will (but please let me know if you solve it!)
I have a John B baptised in Blewbury 15 Sep 1677 s/o John & Mary. John jnr is the one I have marrying Mary Deadman in 1706. He is the brother of my Lucy Blissett and - taking in what LizzieL said about your Richard having a sister called Phillis - John & Lucy also had a sister called Philllis baptised in 1686.
I haven't been able to find a marriage for John B snr & Mary but their first child baptised in Blewbury was Alice in 1675 so the marriage would presumably have been c 1672-5.
I then have John (snr) baptised in Blewbury 21 Jun 1651 s/o Christopher B. So, were there 2 Christopher B's having children in Blewbury and Sutton Courtenay at more or less the same time?
Christopher B married Ann Kimber in Blewbury 25 Aug 1642 (no further info given). I found a baptism in nearby Ardington for Ann: 15 Jan 1616 d/o Richard & Marie.
I have Christopher's baptism in Blewbury 9 Nov 1606 s/o Robert & Elizabeth and his marriage to Elizabeth Stacie in Blewbury 14 Nov 1591. First child is Margaret baptised 1592. It always makes me stop and think that this is the time of Elizabeth I - I think you can easily forget the timeline when dealing with BMDs.
That's it - I haven't found baptisms for Robert or Elizabeth, though I will try and look into the 1572 baptism in Somerset that you say someone has come up with. Do I take it that there was no proof or background to this date?
Hope you can make sense of the above. As I said, plenty of Blissetts to go at and all probably intertwined, but let me know if you have a eureka moment, won't you?