How about the T209-2 B.A. Thompson back? I think it fits your criteria, although it's a bit different in that Thompson is the only card in the set with that back, and Thompson can only be found with that back.
Not my card.
ETA: Looks like there are actually four different versions of the Thompson back: (A) no factory number; (B) stamped factory number; (C) printed factory number; (D) black border. Each one may be unique, or close to it. (Courtesy of t209-contentnea.com)
