I'm not an ADP expert yet but I do have some ideas to share that may help.
The Advanced Device Properties that I've seen have always been attached to the devices in the extracted layout netlist. I'm thinking of the netlist we get from "calibre -spice". These properties were present in the same fashion as "W" and "L" properties.
If you're seeing something different than that, I wonder if it relates to LVS PUSH DEVICES SEPARATE PROPERTIES ?