I am thinking out loud, so correct me if I go wrong, but can I throw the following into the pot for consideration.
You write that Mary Head was the only child of Edward and Mary and the family had a connection with East Grinstead.
If so, a baptism in EG on 2 December 1715 (IGI) would also seem to fit.
As for her father, assuming her parents Edward and Mary also had family Roots in EG, I am drawn to a baptism of an Edward Head in EG on 6 July 1681 (IGI) son of Edward and Elizabeth.
John Taylor/Tailor/Tayler was born c1715 and came from the area around Ripe.
There are no Ripe baptisms that I could find for him, but of others in that area, the best fits from the IGI would have been John of Alfriston baptised 1718 or John of Ringmer baptised 1714. Roy G