The plot thickens....
After reviewing your arcing video in slow motion and reviewing the picture where you were inspecting the contacts something does not make sense.
The switch stack is made up of 5 sets of switches, 3 singles, and 2 doubles.
If you find all these on the schematic they look like this...
Notice how all the single switches are closed. On your unit the switches are all open. To me this indicates that the unit state is represented as latched in the schematic, most others relays are drawn on the schematic as unlatched.
Also, in your arcing video the game over relay seems to keep on trying to latch but is not able to. What should happen is (*) the big coil pulls the switch plate down and then the little metal plate in-front of the small coil locks the switch plate in the 'latched' position. When like this both coils on the game over relay do not have power running through them. Upon a game ending, the small coil is powered and the switch plate pops back up cutting power to the playfiled. Once that step is done, again power is removed from the coil. It stays like this until a new game is ready to be started where we loop back to the (*) above.
I suspect that either the big coil is damaged. Check its resistance with one lug unsoldered, or the little spring on the big coil plate is tight. Either way, make sure the unit is able to latch and unlatch cleanly and you should be at the end of this headache..... for now