I will take a look at some of the information I have that might relate to your line.
John Beard lived near the Williamson , Hickman, Maury Cty lines and the Beards traveled back and forth quite frequently. My research normally shows that the majority of Beards there are related. Although they might not want to claim each other(GRIN)
Although the tie may not be easy or may not exist. John & Mary had a large family, as did their children. They even had a son named John born ca 1805.
Do you have any other information on your family??? I am not prying but if I have the logic used to derive your family tree it could help.