I had two final (well, probably not) thoughts on Daniel Thurston's origin. I spent many hours--days!--on this before leaving on several trips this summer. The first is that whichever potential line I traced back through good or shlocky genealogy, ultimately all appeared to have their origin in Suffolk, not far from the town of Thurston. So, on one level we do know, the question is where Daniel's ancestors went between Suffolk and Newbury.
The second is that my DNA results matched with a number of people from western counties of England: Dorset, Devon, Gloucestershire which would appear to most likely connect to my Thurston ancestors. Although I still think that Thornbury in some ways is the least likely place of origin for Daniel, I do wonder if these matches lend credence to it. For now though, still a mystery.