Check out the line up from Native Watercraft fishing kayaks featuring their propel pedal drive system and YES you can definitely pedal backwards.
TITAN PROPEL 10.5, 12, 13.5
The Titan is a “First with Reverse” Propel Pedal driven bass fishing kayak extraordinaire. Large and in charge, the Titan Propel 13.5 (PATENT PENDING) offers unsurpassed stability and ample room and flexibility to move around. Optimal for sight casting with plenty of leverage to reel in the catch, this is a angler’s fantasy fulfilled. This boat features easy-to-reach horizontal rod storage with rod tip protection. Elevated First Class Seating is designed for comfortable transitions between standing and sitting, and it can be moved out of the way for a walk-around deck. The Titan also contains an interior foam layer which adds flotation for safety and increased stiffness for performance. In addition, the boat features two stern power pole mounts for dual anchoring to further increase stability. The Titan can be purchased with a custom motor mount that will accept trolling motors for a power-assisted ride.