A question, I believe the chime function only initiates on the keypads?
I don't use the chime function myself since I can't hear it unless standing next to a keypad the wife on the other hand seems to have no problem hearing it. We have a long driveway and detached buildings and several driveway sensors so that we know when stuff comes and goes and use relays to trigger electronic doorbell chimes in several areas which don't currently have keypads
I'll be listening for the answer as well.
Your idea with relays is interesting. If it's all right, I may reach out to you once I have my system up and running to understand this a bit better.