I just this summer realized that I have an Addison/Edmonds background in Cornwall and I saw your posts on GENFORUM.
My great grandmother was Ada Eleanor Eva (1868-1890) of Penzance who emigrated to the US circa 1885. Her parents were Rebecca Addison Lanyon (b. 1839) and James Richard Eva (1829-1913) Her maternal grandparents were John Lanyon and Mary Addison Edmonds (1810/12-1877) Her great grandparents were William Addison and Mary Edmonds (b.1785)
That's as far as I've gotten by going through online census records, etc. I'm in Japan so it's a bit tricky. If you have both Addisons and Edmonds from Cornwall in your family, we may have a connection.
My family always said there was a relationship to Joseph Addison and his family, but I can't find anything to support that.
Do you know anything more about either of these families?