Quoted from paulace:

Well, you still have a couple things going on. Obviously, your 1000 pt relay is firing steadily - but not stuck on like your 10 pt relay was, so likely a different problem. Although, since it began after you worked on the EOS score reel switches, I would look again at the one you adjusted and make sure it's opening and closing correctly - but to be honest, an EOS switch won't cause that behavior - it's just curious that it started after you adjusted a switch. Could you have bumped or bent something close by while you were working on that switch?
If you have a schematic, look at what makes the 1000 pt relay fire. I do hear your score motor running constantly too, but I don't know if that's a cause or a symptom yet
Also, when the 1,000 pt score goes past "9", the 10,000 score doesn't increase. That's most likely another switch problem in the score reels. There is a switch on each score reel that closes when the score reel gets to "9" - it's open at other times. Look closely at that switch and make sure it's operating correctly. You can compare it to the same switch on an adjacent score reel if you have one that's working correctly. Look for broken solder joints up there in the score reels also - a loose wire that's just hanging out there.
Look at the attached photos. I would go through each score reel and clean all the switch contacts, look for broken wires - carefully examine them and make sure as you click the score reel around with your finger (by pressing the plunger all the way in, then releasing it), that the switches open and close when they should. I know there are 16 score reels, which makes 64 switches, but they all have to work correctly for the game to work.
Start there and good luck!
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Quoted from paulace:

Thanks EMsInKC for catching those drawings if they're wrong. I don't have a Williams machine nearby to check them. I'll get rid of them to avoid confusion.