There are two paths into the 10s Score Reel coil. One is through a switch on the 10 point relay which is used during game play and the other is through a switch on the Score Reset Relay which is used during reset. A first step might be to divide the problem in half and eliminate one of these as a suspect. If you block both switches with a piece of paper the 10s reel should fail to reset at all. If you block just the 10 point relay switch and the problem persists that would implicate the Score Reset Relay path.

The Score Reset Relay pulses 5 times per 180 degree turn of the Score Motor until the score reels have reset. Watch that relay as the game resets. Does it pulse when you get the extra points? Does the 10 point relay pulse at all during reset?

/Mark

Since you get a variable number of points scored it may be that pulses from one of the impulse switches on the Score Motor (in the red boxes) are getting through to the 10 point relay when they shouldn't.
Teachers Pet 10 pt relay (resized).jpg
If one of the normally open switches in the paths involving the Score Motor Impulse switches is gapped too close it may allow stray pulses to get through. Have a close look at these paths and the switches on the Drop Target relay and the Eject relay in particular.

Tried what exactly? Did you block the two Score Motor Impulse switches to see if that stops the extra points?

When the roll over buttons score more than 10 points can you confirm that the Score Motor turns? I don't think it should for 10 points.