I will add one more observation, which might be of use:
When I tried to use the system with those ultra-cheap super-regen receivers, you know, the ones you see everywhere and are usually paired wit the transmitters, the system simply does not work!
I found that maybe one in a hundred keypresses registers and that's if you make the delay 500ms and then again only for the tri-state type transmitters (2262), not for the regular household alarms/fobs. And, of course, only if the transmitter is physically on top of the receiver....
Quite simply, these little receivers are NOT fit for purpose.
The other one I am using, a superhet with the four pins on either side and the shielded unit in the middle works acceptably well. Of three units I tried, one was a bit short in range but the other two worked as well as you'd expect. I haven't tried proper measurements yet though. The (good) units I'm using are marked RXB6 (2.0), and I understand you can also get RXB8s, though I have not seen them yet.