I can't see a connection right now but I have a John Goadby b 1808 in Market Bosworth Leicestershire, England
He was the son of Joseph Goadby and Frances Mee both from Mkt Bosworth, Leics. However, I do not have them with a son named William.
John emigrated to USA as a Free Will Baptist Minister serving in Poulteney VT.
This information comes from a family tree of Goadby's originating fro the South West of The County of Leicester reaching back to Ellis Goodbye b c/1520. This work was compiled by Brigadier FRL Goadby.
If you can make a connection I can help with the rest.