Did you check to see if there is a spring and the mysterious disc inside of the distributor grease cup assembly? This assembly tames the wobble in the distributor shaft. If the spring is missing, you will have issues like what you have described, especially a distributor with some age on it.
Carl

1952 5-window - return to "as built" condition | 1950 3100 with a 235 and a T-5 transmission