1994 Pontiac Sunbird Starter Won't Engage Flywheel

Sometimes when I go to start the car, the starter will wind up as usual but won't engage the flywheel and turn the engine over. Usually trying a second or third time will engage it and it will turn over as normal. I have replaced the solenoid with a new one, and done a complete rebuild of the starter myself so I know it all works. I replaced the brushes, bushings, and drive, and the return spring works fine. The ignition wire to the solenoid seems fine.

What would you guys recommend checking? I removed the plastic cover to get to the torque converter, and the flywheel looks fine, not a mark on the teeth. Could the starter need to be shimmed? If so, how do I go about doing that, because I'm not sure exactly where to put them. The only other thing I can think of is the starter drive isn't engaging far enough sometimes. Somehow. Any advice would be greatly appreciated!