I will re-read what you said, and look some more tomorrow. I'm incredibly tired tonight.
I looked through the schematics last night until very late, and finally (mostly) understand the relationships between the ball count stepup, player unit stepup, and player unit reset. Basically, the outhole relay will always trigger the player unit stepup, and the matching connections on the circuit in post #3 will trigger the ball count step-up. If the player reset relay is active it will also trigger the player unit reset relay (setting back to player 1). I'm too tired right now to remember what conditions do this, but it made sense last night.
So,... if we eliminate the coin unit from the circuit (post #3), each ball drain will trigger the player unit stepup until player 4. Because the player 4 setting on the player unit bypasses the coin unit, when player 4 drains it will trigger the ball count stepup and the player unit reset.
I isolated the coin unit by putting paper under the wiper contacts associated with this, essentially removing all of the connections on the right side of the coin unit in the circuit in post #3. If I hit the start button once and then activate the outhole, it works exactly as expected - the player unit advances and the ball count does not increment - until player 3. The ball count stepup is being activated for both player 3 and player 4 (the player unit reset works correctly after player 4).
As you can see in post #3, the ONLY way for the ball count stepup to be activated with the way I set it up is through the R-W wire from the player unit. The only way for it to happen with player 3 is for R-G-I wire from the player unit to be shorted to the R-W wire. I checked with an ohm meter, and don't see any short. The only other explanation is the wiper in the disc momentarily bridging the rivets for those wires.
Maybe tomorrow I'll know more.
Thank you very much for your continued help.