I am somehow related to the William T Pate family you listed. I am a member of the Pate DNA group, and matched this family very closely. My ancestor was Calvin Pate, b. 1811 TN, lived in Rutherford - Bedford area, moved near Dukedom in Weakley Co in early 1840's before moving his family to Texas ca 1857.
Can you send me the contact info on the administrator of family's web site? email is brupat4520@sbcglobal.net.

Thanks,

Bruce Pate