1966 3Speed LKM Washer
It could either be a mechanical binding condition, but if it runs through cycle A or B [ all hi speed motor operation ] fine then I think you might have an electrical issue with the timer or possibility the extra motor speed switches on the back of the mechanical push-button mechanism. It is normal whenever this washers motor starts for all three speed indicator lights to flash on for a split second or for them to stay on if the motor is stalled.
I would try removing the belt from the motor pulley and running the motor through the parts of the cycle where the washer has had problems, you will have to attach a small piece of tubing to the water level Sw and blow into it and pinch it off to get the motor to run in the agitation periods. It is possible you got another bad motor or maybe neither motor is bad and the timer is faulty, Good Luck, John.