I don't know if this will be any help. I too am struggling with a family connection. The following information is on Joseph A. Beard, son of John Mason Beard. I there is a connection, I have much additional information to share.
Joseph Alexander Beard Born: February 28, 1827 in: Kentucky Died: September 26, 1906 in: Brownville, Nemaha, Nebraska
Father: John Mason Beard Mother: (Unknown)
Wife: Elizabeth Richardson Born: January 1826 in: Illinois Died: Aft. September 1906