It's been quite a few years since these posts were made, so I hope people are still being notified, or interested in this line of inquiry.
Jerome R. Head was my grandfather. My family has an essay that is similar to the book mentioned and has similar content. I do have a pdf of the book for anyone who is interested. As far as I know no one has been able to trace Solomon Head's father, so to able to see the letter you have would be interesting. I don't remember my grandfather ever mentioning that he had found him (Solmon's father). This would also be crucial to linking my family with the Heads of Rhode Island; although DNA would probably be the way.
All of that being said I do have information on Solmon's family descendants, should anyone be interested.
Emily Head
ehead@northwestern.edu