There's some relatively older neighborhoods around the LA area that were built in the 40's that use low voltage switching. Years ago I did a couple of service calls on these. These were somewhat unusual in that the relays were not located together but were distributed throughout the house. For instance, a switched light outlet would have the relay stuck in a KO in the outlet box - HV wires inside the box and LV wires out in the attic space.
I did not run into the situation you described (sticky relays)but I did replace a few burned out relays and defective switches. There was an Ace Hardware store in the neighborhood that stocked relays and switches and sold them to all the neighbors for outrageous prices.
If you discover all the relays in a common location, there is some benefit to that. As I understand it, the downside to that is being able to hear the relays all operate at the same location (i.e. if the relay panel is located right above the living room). However, it sure would be easier to work on.
Good luck, and please report back your findings.
Radar