Since it's the exact same iffy-ness for all players, my guess would be the switch on the 100 relay up there is most suspect.

Clean the player unit contact traces there with a scotchbrite pad or similar if you haven't. Make sure the switches in the 100 relay have a little bit of extra travel after they touch and clean them with a few light swipes of a fine file. And check those wiper arms on the player unit in case one has been bent backwards or sideways and not making strong contact with good pressure, or the contact is not centered on the traces.

How about id'ing the pair of player unit wipers responsible for the 1000 pts. circuit, by putting a snip of paper under them and scoring 1000 to find them. Then use alligator wires from those two wipers to their own lugs on the board just to remove that as the source of the problem as you test the 100 points more. Did you clean the 100 pt relay switches?