Well, that was the wrong pitch
I got it figured out though, 1.25mm pitch, not 1.0. Unfortunately, I can't get any 1.25mm pitch samples from Molex, but I believe they should work. Also, Molex doesn't have SMD connectors in the 1.25 pitch, so no drop-in replacement. Kyocera has a line of 1.25mm SMD FFC connectors, but they only go up to 20-contact. http://www.kyocera-connector.com/prdct/type/fpc/6207.html
So close, yet so very far away...
Also, incidentally, the same cable in an 11-contact version is what is used to connect the SNES controller jack daughterboard to the mainboard in the old, large SNES models.