I have added the register report, "Nathaniel Briggs of Block Island" to the "Files" folder at the Yahoo Group called "tauntonbriggs"
It is taken from the 75 page "book" that is the work of Lila Briggs Sampson. It was typed and placed in a few libraries, including the Wisconsin State Historical Library, where I found it.
I know of no other book treating the Briggs family that came from Block Island, and searches online convince me that much of the content is unavailable to most people who don't live near one of the few copies.
It does include the Joseph Briggs of Block Island, RI, and his ancestors & descendants.