I have resolved the issue and hopefully this will help someone else down the road. I went back through the manual to isolate where the reset was failing:
"The 1st player score unit resets to zero through the P3 switch stack on the player unit and motor switch 1A. When these units reach zero the player unit steps once, the 2nd player score unit resets to zero through the P4 switch stack on the player unit an motor switch 1A."
So I targeted the P3 switch stack on the player unit in the backbox. I manually dialed up a score and reset the game. I quickly manually engaged the entire P3 switch stack and kept it engaged until all the Player 1 reels went to zero. So this told me that the P3 switch stack and the reels were working correctly.
Working backwards through the previous step from the manual, I moved onto the motor switch 1A in the cab. This was the next logical place as the P3 switch was working but not staying engaged long enough to reset all of the reels. So I cleaned and adjusted the 1A switches on the motor and this resolved the issue. So my guess is that one or more of the 1A switches were barely making contact allowing for only one pulse to the P3 switch stack. This intermittent connection stopped the score reels reset prematurely.
Thanks for the feedback!