Best way to do this is one problem at a time. So #1: Since all 3 ROs are affected, those switches are likely ok, but give them a good check anyway. They should make solid contact and be nice and clean. Then check the switches on this relay for the same thing. It is also possible that score motor sw. Impulse-C needs to be cleaned, so loosen the sw. stack screws and check that. Also, don't run amok cleaning everything or you can create new problems. And do you have a high-quality schematic scan you can post? IPDB does not have it.
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Last one or two of the stacks that make up the score motor. Lettering starts at the bottom. The schematic, which you need to buy, shows it and what each sw. does. Snippet is from a Ding Dong, but all Williams follow the same pattern.

On your logic: sw. A on the 3000 relay keeps it energized
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PBR would have it. http://www.pbresource.com/

Ooops, should have mentioned that ... you could try Marco.

Could be the Lock relay and/or Game Over relay M/B sw. (for player up, yes?)

Williams Ball Index relay will do that.

https://www.marcospecialties.com/

Try the middle two sw. on the Lock relay for the lights.

OK, losing it ... first thing I thought of this morning was that the Lock relay sw. would involve the whole backbox. Check the M/B on the Game Over relay.

Check sw. C, and if not that, the coil on the chime box. Did you check that Impulse sw. for the 3000?

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Email Jimmy at [email protected]

Be interesting to see what else is involved once you get the schematic. Can you take it to Staples when you get it, have it scanned and saved as a PDF and post it here? $2. Bring a thumb drive.

Try doing a jumper from Imp-C to the sw. on the 3000. You could have a cold solder, bad wire, etc.

It could also be that not all of the pulses are getting thru.

It should answer many questions. I had to read and re-read your last post a number of times and still not sure I got it.