I did a few calculations, and the bearing loads on the encoder from the swinging pendulum are going to exceed the maximum loads specified for the encoder. I don’t want to destroy the encoder, so I decided to redesign the cart. I added a bracket on top of the cart that extends out beyond the gear. The encoder will be mounted on this bracket, and the pendulum will be almost flush to the bracket. This will minimize the loads on the encoder shaft. Time for some more cutting and drilling, I guess.
Inverted Pendulum Design v2 (pdf)