As mentioned, you should really be using a solenoid for each piston, we found that attaching them directly to the shooter worked better. Additionally, you may want to move your pistons farther towards the pivot point and start the catapult at a lower position. It sounds like a weird thing to do but when the catapult requires a greater amount of force to move initially it causes the air to build up in the piston first, basically doing the latch thing without an additional mechanism.
Here's a video from our first prototype, we currently have two pistons that I believe are the same size that you guys are using. You may also want to check out 842's design, they have a great pneumatic shooter.