Identifying these light switches
These are really old HAI switches (from before Leviton bought them) which use the ALC protocol over separate signaling wires.

I finally found someone who could tell me that the original switches were put in around 2005, so I used The Wayback Machine to look at HAI's website as it appeared at that time. From there, I found pictures that match these switches perfectly.



UPDATE: I finally got into the controller cabinet for the system and discovered that it has an ALC controller already hooked up with lots of wires that appear to go to these old switches all over the building. It appears that we should already be able to control the old switches from the system because of this board, so I'm guessing that something is just misconfigured in the settings.