I have a working single Stewart platform prototype, which is capable of motion.  My super simple script now just moves all the axes to one of two alternating positions with different commanded maximum accelerations.  That's enough to verify that it is able to operate repeatedly and that it can make decently high tosses.

Next up is implementing the IK for the Stewart platform so that I can get aiming working, and possibly also improving the mounting so that it doesn't jump around so much for high tosses.