I am certainly interested in the information you are willing to share. I can give you information regarding Joseph's brother James' line if you like.
My g-uncles Charles and James (Jim) Rayment used to visit and correspond with Rayment relatives in England during WWII and afterward. They are twins and both fought in the 2nd world war. I am told by my cousin (Charles' daughter) that they visited a place near London and one of the cousin's names she mentioned was Eddie Sharp. Does that info ring a bell for you? I have written my g-aunt (Jim's wife) to see if she can shed some lite on this for us. She just turned 93 yrs old and still sharp as a whip :-)
Perhaps we can correspond directly. My email is firstname.lastname@example.org. Looking forward to hearing from you soon.