Installed old starter bendix on a rebuilt starter and it has locked up twice just this week. I pulled the access plate and everything looked fine, but I did that after I got it unlocked.
Just a swag, bad ring gear. Look at the teeth on the ring gear on the flywheel.. Dan
The starter shaft probably is either bent or it has a burr on it that needs to be dressed with a file. The shafts are easily bent and easily straightened.
When you check the ring gear, look in the side where the bendix bolts on. rotate the crank very slowly so that you see every tooth on the gear. The edges on the side toward the bendix should be beveled and not worn. If you find areas that are worn, those are the areas where the starter will stick. Unfortunately, the engine tends to stop in one of two positions every time the ignition is shut off. You might get some help if you turn about a quarter turn with either the crank or by pushing the car in gear, before using the starter so that it will hit the flywheel in a different place. The bendix gear is also beveled and if it is worn would also be a possible cause of the problem.
The only sure cure for a worn starter ring on the flywheel is to replace the gear. That would require pulling the engine out of the car. So you could use the hand crank or push start the car until such time as you are ready to pull the engine. I would also suggest that if you do pull the engine you go through everything in the engine, transmission and magneto to make sure it is in good condition. A few dollars spent when the engine is out will save a lot of labor in the future.