"[...] radio-based system cost about $250 [...]"
433mhz transmitter/receiver modules for this sort of common radio signalling are only one or two pounds/dollars. Combine them with an Arduino UNO or NANO and you are away. Under $20 I would think.
I have that combination spoofing my Byron door bells and PIR detectors. It rings the door bells dotted round the house with one chime if someone approaches the house. It uses a different chime if they press the door bell.
Biting the hand that feeds IT
