I'm happy to report I got it working!
These parts were fun to make. There's a trick in the counterweight -- the groove fakes out the eye so you can't tell if I matched the outer diameter exactly on the top and bottom halves.
The complete arm assembly, screwed onto the servomotor "horn":
The servomotor, with mounting hardware. The scrap of paper is to keep a set of shim washers in place; the washers transfer the weight of the arm to the case of the motor, so there is no axial load on the mechanism. The counterweight eliminates any side load on the shaft.The whole arm/glass during operation could weigh nearly two pounds!
Finally, here is (bad) video of a motion test:
