Relay logic with no prints... tough to troubleshoot over an Internet forum. I can't help you out about prints, but here is how I would approach it:
Answer these questions:
Are intermediate floor calls latching?
Is the problem directional, or does it occur in both directions?
Assuming that intermediate floor calls are being latched:
The first sequence of events for the stopping circuit on most relay logic hydros is for the selector to step. Are there any relay acronyms that clue you in to see if the selector is stepping? Maybe 1P, 2P, 3P, etc.?
If the selector is stepping properly, the next step in the stopping sequence would be to drop high speed. Again, any acronyms that might be the high speed relay? H perhaps? Is the high speed relay still picked with voltage as it passes by the intermediate floor where a call is registered?
After high speed is dropped it should start leveling when the selector sees the leveling vane for that floor, and stop by dropping the main direction relay (U or D?), dropping the level up or level down relay (LU or LD?), cutting out the motor and up slow valve coil when the level up sensor comes off the vane (for up direction), or by cutting off the down level valve coil when the level down sensor comes off the vane (for down direction). This step is obviously not happening.
I would check all the relays, and stepping vanes that may be associated with the functions in that stopping sequence. May be relay contact failure, or a bad stepping switch on the selector.
Most elevators will slow down to stop at the terminals even if they are not stepping because of the terminal slow down switches actuated by the car cam.
Hope this helps, good luck. This would be a fun one to troubleshoot with prints, I'm sure you would have it fixed by now if you had prints.