UPS flies down there nightly. You'll also find Gemini down there occasioanlly, as well as Florida West. I also understand that Cielos goes down there regularly, but they're a 129 operation, so I doubt that you'll get there on them, but it's worth a shot. Forget FedEX- they're running Mountain Air Cargo F-27's down there out of Campinas, Brazil. No joy with that jumpseat.
But seriously, if you're in the CASS system, why don't you just take American, United or Delta? They fly down there everyday?
No, technically, you're correct; CASS was SPECIFICALLY designed to allow COCKPIT jumpseating on other carriers. However, many of these carriers have simply written their policies to only allow CASS participants a jumpseat, whether it's in the back OR in the front of the bus.
Prior to 911, it was based on reciprocation; you have a seat available on your bird, so we'll offer you a seat with us. After 911, most of the reciprocating agreements went out the window. However, if you get put into the CASS system, you have, by definition, a seat available to trade, and that saves everybody the hassle of getting reciprocating jumpseat agreements between all the different airlines.