As Dan says, the Catrike isn't designed for a kick-back hub. You need something that keeps both the top and bottom runs of the chain under tension to keep the reverse tension from derailing the chain. Your picture shows that the return run of the chain is very loose- it really needs to be improved.

Does the return run of the chain run over a pulley or through a chain tube? If it's the stock setup, then it runs through a chain tube. In that case, there's no good way to tension the return run of the chain. The chain tube will create a bunch of friction if you put tension on it.

I would replace the bottom pulley with a pair of pulleys, one for each run of the chain. I would also install chain keepers on both pulleys to keep the chain from ever coming off either pulley. Since you're relying on coaster brakes a derailed chain means no brakes- not a good thing. Terracycle makes chain pulleys and keepers of all sorts and they're used to coming up with custom solutions: Idlers : TerraCycle, Exquisite Recumbent Parts & Accessories

After installing the two-pulley system, I'm going to suggest you extend the boom enough to keep the chain under tension on both the drive and return runs. This will compromise your leg-length adjustment, though. Your frame wasn't built to adjust the rear wheel position (like Dan's upright bike) so you have to accept some compromises.

The alternative solution is to abandon the kick-back shifting. Do you have enough mobility/dexterity in your hands to shift gears? There are setups using a one-way clutch on the cranks that pull a cable to operate brakes. They are used on handcycles to allow paraplegics operate their bikes/trikes. Here's a video of one in operation:
A friend has a similar setup on his hand-and-foot powered recumbent bike. It allows the bike to have backpedal brakes and a Rohloff internal gear hub (although it would work with derailleurs also).

Good luck on your endeavors.