Hi Will,
For problem #1, I wonder if the switch on the AX relay that affects the 10's resetting is stuck closed for some reason. The first snippet is the reset circuit....just 3 switches involved, and the Motor 1A switch is common to all the reels, so it's probably working correctly. That leaves the "10'S UNIT RUNOUT" switch that should open when the score reel gets to zero, and the AX switch that should open when the reset is complete. I wonder if the AX switch were always closed, if you'd have the score reel just lock on until it got to zero, which would open the runout switch to break the circuit.
volley problem (resized).JPG
The EOS switch on the score reel doesn't come into play during the reset - only when the 10 pt relay (N) is involved in scoring. It breaks the current to the N relay, but the N relay isn't involved in the reset circuit. And since your N relay isn't locking on, it seems to be working correctly. While in the reset process, with the 10pt score reel solenoid locked on, is the N relay also locked on?
volley problem 2 (resized).JPG