For that reset problem - here's the circuit that makes the score reels reset to zero:
ED reset circuit colored (resized).JPG
When you start a game, the S relay fires, which switches the m/b S switch on the right side. A switch on the S relay starts the score motor, so when the Motor 2C switch in green closes, the A relay fires (via the green path), which closes all the green A switches above. S de-energizes at the end of the score motor cycle, so the m/b S switch is then as drawn on the schematic. A is mechanically latched on, so it doesn't need to be powered after it latches.
A switch on the A relay turns on the score motor, so the score motor is spinning and the Motor 1A switch in red is opening and closing 5 times for every 1/3 turn of the score motor. The 4 runout switches (1 on each score reel) are closed EXCEPT at zero. The green A switches are closed now, so each of the Motor 1A pulses can go through the A and runout switches on each score reel to make them turn. When they reach zero, 2 switches on the score reels change state - the runout switches open (which stops further pulses from getting through and making them turn), and the red Reset switches on the bottom line of this snippet close. So the Reset and Runout switches are now as shown on the schematic.
Now that the reset switches are all closed, when Motor 2B closes (late in the score motor cycle), the AR (Reset Completed Relay) fires (via the red path). The A and AR relays are interlock relays - on the same housing - which means that when one latches, the other releases. So when the AR relay fires, the A relay relaxes, which opens all those green A switches and stops the score motor from turning after it completes its last cycle.
A relaxing also closes that n/c A switch in your O relay circuit (top snippet of post #2), so the O relay can fire as well and your first ball gets kicked out.
So if your score reels aren't making it all the way to zero, it could be that your A relay is relaxing too soon due to the AR firing early - possibly because of misadjusted Reset switches that are closing early....or possibly the Runout switches on the score reels aren't adjusted correctly and are opening early.
You might have some score reel switch cleaning/adjusting in your near future. Luckily, you only have 4 score reels!