The 10 points being awarded and the hot chime coil suggest that the 10 points relay is staying engaged when it shouldn't. How does it behave compared to the 100 and 1000 point relays during startup? And what about the ball index relay? Does it stay engaged? It looks like it would if the 10 point relay is staying engaged and then there is a NO switch on this relay that would keep the ball count unit s.u. coil firing until it reaches game over.

I just tried starting up my machine while closing one of the 10 point switches on the playfield and the ball count unit advances to the second ball and 10 points are awarded, but then it stops at the second ball and the ball count unit doesn't step all the way to game over. And so given the difference between my result and what is happening on your machine, perhaps too there's a switch that is closed that is keeping the score motor running on your machine (which isn't happening on my machine when I close a 10 point switch during startup).