82A,
The worn bushings are quite likelly, as you suspect, to be the problem. You said that you were able to move the distributor shaft back and forth in multiple directions. There is another check that should be made.
Grab the advance retard arm of the upper plate and attempt to move it horizontally by pushing the arm and pulling on it. I don't mean in rotation as normal, but toward the radiator and firewall. The idea is to check for play in the upper plate at the center hole. This can affect the points also. It is a less common problem to find, but I've seen it posted before.
Another issue that is known, but less often found is that the brown insulators that are riveted to the plates can become loose under their rivets. This allows intermittent shorting problems. Check both plates to make certain the insulators and their rivets are still immovable, tight.
In hopes of learning something, I'd be interested in knowing what the ammeter is showing when the car is stumbling??? If the 1929 November service bulletin is applied, the functioning of the primary ig circuit is visible on the ammeter. The ammeter is your friend in the Model A and should be monitored as you start the car and immediately on engine malfunction.
Good luck and hope this helps you.