If this locking-up condition occurs often, then the starter shaft is undoubtedly bent. This happens over time when people forget to retard the spark lever while attempting to start the engine. Depending upon how the initial ignition timing is set inside the distributor, it may too far advanced so that the engine "kicks" back when it catches and jams against the starter's shaft. Enough of these incidents and the shaft will bend, causing what you are experiencing.
To check the shaft, remove the starter (again!) and Bendix drive. Hook the starter up to a 6 volt battery or heavy-duty charger (not a trickle charger or to a battery tender) via jumper cables. It won't matter how you orient the cables, although for consistency's sake the red cable should be attached from the battery's positive terminal to one of the starter's mounting ears as a ground. Connect the black jumper cable to the battery's negative post and touch the other end against the broad brass terminal on the starter. Once connected in this manner, the starter will turn over a high rate of speed. The shaft should spin straight and clean, but if it looks fuzzy and out of focus, the shaft is bent. You can straighten the shaft in a vise or replace the armature. Be sure to hold onto the starter firmly when testing it this way because it will want to take off across the floor from the spinning torque created by the applied juice.
As stated in a previous post, you will probably discover chipped or missing flywheel teeth because the Model A engine tends to come to rest in one of two positions 90% of the time (an estimate) when it is stopped. That means, the starter drive bangs at high velocity against those same two sections of ring gear teeth 90% of the time, usually 180 degrees apart. Eventually that will grind the teeth away, effectively making it more difficult for the Bendix drive to engage the teeth to turn the engine. Not much you can do to permanently fix that short of pulling the engine and flywheel and then replacing the ring gear, or as some guys do, heat the ring gear and rotate it 1/4 of turn to present a new set of unused ring gear teeth to the Bendix drive. A lot of work and expensive acetylene gas just to save $20, though. In the meantime, you can "trick" your engine and instead of letting the crankshaft come to rest where it wants to, keep the car in 1st gear, push down on the brake and slowly let out the clutch. The engine will die. Then be sure to turn off the ignition key. You are basically killing the engine in an unnatural place so that the crankshaft will usually end up in a different place than it normally would on its own. This places the Bendix drive against undamaged teeth. Don't abuse the engine too much this way until you can fix the problem. It's just a temporary way around this irritating problem.
The final ad hoc thing you can do until the ring gear can be replaced is to use the hand crank to rotate the crankshaft a few degrees the next time you are ready to start the engine. Once again, this will put an unused batch of ring gear teeth in alignment with the Bendix drive. It won't help, however, if the starter shaft is bent. Aside from weak operation, you may be facing two additional problems with this starter: a bent shaft and damaged ring gear teeth.
All of these suggestions do not obviate the need to re-straighten the starter's shaft and replace the damaged ring gear. They will just get you through some rough times and potentially embarrassing moments until you can make permanent repairs.
Marshall
