I'd start at the 10 point relay and give the contacts a clean with a business card and then check the gap on each contact.
Done that - this got the score reel resetting. I have cleaned the contacts several time now and adjusted the contacts to the point where I am pretty sure they are spot on. Could the relay coil have been damaged when the 10's score reel coil was cooked? It half seems like at times the relay contacts aren't all activating, I don't know whether the coil is intermittedly not pulling on the plastic surrounding the contacts hard enough.
