Check your EOS switches on the score reels.

Here's a wild theory and the schematic to explain it:
Aztec 100 point relay (resized).jpg
Any time the 100 point relay fires the lock in switch on the 100 point relay in the lower red box closes and keeps power applied to the 100 point relay until one of the four 100 point Score Reel EOS switches opens. That seems to work fine most of the time.

If the problem only happens when 900 points rolls over to the next 1000 points then the path through the Player Unit must be involved somehow. Usually there is no path between the yellow wire on the left side and the O-Blu-2 wire connected to the 100 point relay switch in the upper red box. However once the 100 point is about to rollover the yellow and orange-blue wires get connected together so the next time the 100 point relay fires the 1000 point relay fires too.

Notice that both switches in the red boxes are on the 100 point relay. When the 100 point relay fires both of those switches close. If the switches are damaged, or if their solder tabs or wires are shorted together you could get the relay to lock on as you describe. Since the yellow wire is connected to the O-Blu-2 wire that means that the yellow wire is effectively somewhere in the 100 point relay switch stack. If it touches some part of the lock in switch it could keep the 100 point relay stuck on even if one of the Score Reel EOS switches open.

Have a close look at all of the wires, solder tabs, spacers, contacts, etc. on the 100 point relay and see if anything might be touching something it shouldn't.

/Mark