I may have missed this.....There is a switch blade on the score motor that acts as a brake for the motor. If that blade breaks off, the motor will spin constantly. This is a common issue with Gottlieb score motors. If the "brake switch" does not do its job, the score motor will overrun its stop position and reactivate the motor looking for the next stop position which it will also run past etc. etc.
Something simple to look for and rule out. It is on a mount all by itself and has no wires running to it. The blade should "grab" a pin on the motor plate at each of the three stop positions.