Hi; I just saw your correspondence on Clarissa Hubbard Brayton and have a little information on Joseph. While in Hemmingford, Quebec, looking for information on Charles Brayton, I saw the pay rosters for the local militia of 1838. There were three Braytons enrolled; Joseph , Sandford, and Charles. The only other Brayton of record was Comfort, and a young Comfort who died at the age of nine. Charles, my ggrandfather later went to Franklin County and his signature is on a will. It matches that on the pay roster. You might find the same with Joseph's signature.
I believe the mill was probably at Brayton Hollow, just outside Burke NY on the Chateaugay River.