Great find L! Just wondering what evidence you've identified to suggest that Edward Baynton remained in England? I've actually being trying to figure out where he ended up... I assumed he died young since I couldn't find him but maybe he left with William?
RE Y-DNA, you could confirm William's parentage by finding another descendant of John's and checking whether they are a close Y-STR match of a descendant of William's. I've been able to use Y-DNA to confirm my line going back to the 1500s. However, it may be quite difficult to find anyone that's tested their Y-STRs. But even knowing someone's haplogroup as reported by 23andMe can be enough to make John and Abigail good candidates, that is particularly so if the haplogroup is rarer.
I can give a real-life example. Last year or the year before, while also looking for a child of one of my ancestors, I found that someone had linked Aaron Rawlings, an early settler of Anne Arundel, to my family on an Ancestry family tree. I ended up researching his life and found a great many similarities, including the names of his children (Daniel, Stephen and Moses), the fact that he named a parcel of land 'Wiltshire', his religion (Quakerism) and the fact his reported age at the time of his passing yields the same birth year as his baptism. I ended up tracking down a living descendant of his, asked if they had done a 23andMe DNA and if so what their haplogroup was and it turned out to be the same as mine. It also helped that my haplogroup is relatively rare.
Of course, it could be that the haplogroup shared by any Gerisshes found is quite common and also given the rarity of the surname, who is to say that most Gerrishes don't belong to the same genetic family? So I wouldn't consider a shared haplogroup a confirmation of my theory, but I would consider it some additional evidence that lends more confidence to the theory.
EDIT: Just a thought, I might check if any Edward Bayntons popped up in Newbury around the same time as William... That would be very interesting since its an even rarer surname (according to Forebears).