Does the score motor always turn just 120 degrees, or 1/3 turn when you press a 50 point rollover switch? Or does it turn a full 360 degrees or a complete turn when the score motor 4E (not E4) switch is activated?

What are the O/5 point and P/50 point relays doing in each of the three cases? To score 50 points, the P/50 point relay should fire, and the score motor should run for 1/3 of a turn and then stop, and the P relay should relax. The O/5 point relay shouldn't fire.

If you remove the 3/5 ball adjust jones plug does the scoring behavior change?

/Mark

Excellent observation. On a 50 point rollover, the O/5 point relay shouldn't fire. What may be happening is that your Make/Break switches at Score Motor positions 1E and 4E are out of adjustment. When working properly a Make/Break switch moves the middle blade between the two outer blades. The middle blade should never in its travels make contact with both outer blades at the same time. If your switches at 1E and 4E are allowing all three blades to contact at the same time they might allow the O relay to fire through the highlighted path shown here for 1E (or the similar path through 4E not highlighted):
Happy clown 5 pt relay (resized).jpg
With the power off, slowly turn the score motor by hand and watch those Make/Break switches to see if all three blades ever touch.

Another possibility is that the switch on the P relay shown in red isn't opening when the P relay fires which allows the O relay to fire when it shouldn't. Check that it opens and that there's no short, solder blob, or bent tabs to keep it closed.