That heating solution works really well, thanks @Shaneb. My first virtual device too. 
So, for the past couple of days the network has been:
2x AlertMe Buttons
1x AlertMe Keyfob
1x AlertMe Lamp (Repeater)
1x AlertMe Power Clamp
3x AlertMe Smart Plugs (Repeaters)
All completely stable and VERY FAST to respond, even after hours left unused.
Oh, and one other device:
1x Xiaomi Mijia GZCGQ01LM Zigbee 3.0 Light Sensor using @markus's driver.
This is the second 'rogue' device I added to the AlertMe-only network for testing. It's been perfect. It only reports changes in level, so it's not chatty all the time, but I've just noticed it perform its check-in. I'm impressed with this one.
I mentioned it was the second interloper. The first had to be a Xiaomi Aqara WXKG03LM Wireless Switch, again on @markus's driver. This one dropped from the mesh within 90 minutes, eventually just doing this.
Because IKEA Trådfri devices are such good citizens I'm tempted to throw a single lamp onto the mesh, see how that behaves, but also pair the WXKG03LM again and observe how long its almost inevitable demise takes. 
