For your consideration regarding parentage of John Joseph
There were 2 farmers in Virgil NY 1850-1870 census, possibly there earlier but I only checked census listing birth place and family members
William Lang, born 1797 in England and Thomas Lang born 1798 in England. Thomas had a second wife and they named their children Mary, John, William, Thomas, Charles (his middle name other records Henry) Thomas named a daughter Mary.
Your John Joseph named his children Thomas, William Henry, George, Charles, Mary
These old families kept first names through the generations. Your John Joseph was a farmer.
I think William 1797 and Thomas 1798 were brothers. Since Thomas named a son John born 1836, your John Joseph likely was the son of William.
I can't look for wills etc because I have visitation with my son this afternoon and tomorrow so I have to barbeque. and anyway, I like to torment and torture you