Hello Dawn, I have just found your message. I too am a descendant of Jonah Beckwith and Mary Callender/Calendar and, before that, of Jonah and Ann. My great, great-grandfather, George Beckwith, 1786-1844(married to Margaret Stevens)was a younger brother of your Joseph(married to Jane Pittard).
I have a lot of information on this family. Do you know they were all silversmiths in the City of London in the 18th and 19th centuries, though George moved to Edinburgh, Scotland and had his family there?
If you email me directly I will be happy to share this with you. Do you have information on Joseph's line?