Ruth, I am also searching this line. As you already may have seen, Burke's Peerage (p.523) records a John Barker of Haughmond, Salop (Shropshire) marriage to Elizabeth Hill from the line of "Hill of Court of Hill." It is my understanding that he is an ancestor of the original James Barker of Newport, RI via descendancy: Edward Barker, Rowland Barker, to James Barker who died in transit to RI aboard HMS Mary and John in 1634. I suspect we share an interest in John Barker's pedigree with a large number of the members of the Barker list.