I haven't had this game in over 15 years but if memory serves me..... The relay that adds a ball, (strike), in the backglass is underneath the playfield and close to the middle, check this first. Manually pull the relay armature open, (turning it off), and if it wants to pull back in, there is probably a rollover switch on the playfield accidently making, (and not cancelling), that is keeping it energized.

The 50-point relay that is scored when a strike is added is probably what is keeping the score motor constantly turning.

Not sure you fixed your problem. I just restored a Bowling Queen and went through every switch and relay. First check that one of the wire forms on any of the 12 rollovers is not stuck. Then as Boatcat said check the switches on the associated relay. Look at both relays involved in advancing a backbox ball. 1. The G Relay (Ball Rack Advance unit) with 3 normally open sws on this relay. 2. Also check the P Relay (Series relay) with 4 normally open sws. Specifically the Red-Gr wire sw on the P relay.

Check "game over", and "tilt" relays. Playfield power runs through both of them.
What was causing the ball rack coil to stay energized?

Credit unit has very little bearing on game operation. You seem to be overly concerned with it. All it does is keep track of credits, and allow the game to start with the start button if there's anything other than no credits.