Nathan, I cannot tell if I can connect to your line of Binfords with only the names provided. However, I suggest you attempt to locate your line through the work of Mary Ladd Binford Bruner and her two important early works: "Binford Family Genealogy" (Wm. Mitchell Printing Co., Greenfield Indiana, 1925) or "Supplement to Binford Family Genealogy" (Metropolitan Printing Co., Portland, Oregon, 1935). Both of these books are available as reprints by Higginson Book Company, Salem, Mass., 508/745-7170). I think I obtained my copies of these books through Barnes & Noble out-of-print service: http://www.barnesandnoble.com/
Mary L. Bruner traces several Binford lines from the 1635 forward in the colonies. Good hunting.