So that's a very interesting one. Since there are two separate stepper units (one for green, one for yellow), the first inclination is to look for something in the circuit that's common to both paths.
Each "Add [Green|Yellow] Advance Unit" is stepped via a switch closed on their respective Advance relay, a series of four(!) normally closed switches around the score motor, and pulsed by a switch at score motor position 1A. The latter switch is the one that would be able to provide five pulses, so four of them apparently are working, instead of just the expected single pulse.
Now, the Yellow and Green Advance relays each have their own lock-in switch, which will keep them energized, but share a common path to release the lock-in.
This suggests that the series of four score motor switches are staying closed, along with the respective Advance relay lock-in, during four pulses of score motor switch 1A.
So one thing to observe is whether the X and Y relays (the Advance relays) are indeed activating and staying locked on for the duration of the score motor turn (or at least four pulses worth). They are held locked in via a switch on their own switch stack, and either a switch on P, or at score motor position 4C. So for example, if the P relay also was stuck locked on, then it could in turn cause either X and Y to stay locked on, which might allow the stepper advance path to complete the four times. So if X and Y are staying locked on, then another observation is whether the P relay is also staying locked on for the duration. It may also be beneficial to try blocking the lock-in switches on X or Y, and P, to see if the behavior changes (or goes away).
Another thing to check is the dog bone switches on the score motor, to ensure they are in the correct slots (S or L). Having one or more in the incorrect slots will mess up the timing, and goofy things can happen.
Those are some initial thoughts. Knowing how X, Y, and P are behaving will help further isolate.
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