Lisa, I hope you get this message. We are doing a genealogy on the Benbows in Jamaica who we were told were descended from the Admiral who is buried in Kingston Parish Church. But his time there seems short for him to have deliberately started a family there (though not totally impossible!) considering he had a wife and family back in England.
A theory re the line, just being put forward, is that when Richard "disappeared" from England he went to Jamaica...that's where his father was buried and the economic possibilities were great. So it is possible the male line was continued through Richard.
There are several records of a Richard Lucien Benbow who I am surmising is a grandson of Richard, son of the Admiral. Richard Lucien from all the info I have gathered seems almost without a doubt to be my grandfather's grandfather, given where he lived and the name "Lucien" being my great-grandfather's (Richard's son) middle name and also that of an uncle. The name "Richard" is also a link though less so than the "Lucien" connection.
When I do a possibility check of the succeeding generations of Richard (Admiral's son) there is a "5th generation" link to my grandfather's father that we always heard about. All of his is to be verified by proper check of the birth etc. records of course.