Jack, thanks for some food for thought. I am trying to accomplish a system similar to your simple sensor network, the difference being the routers wait for the coordinator to ask for light and temperature data. I enjoyed your web site.
With 1 coordinator and 3 routers, all indicate association, slow blink on coordinator, fast on routers. I could not talk to any until I unpowered 2 routers for some period of time, then I was able to reconnect with the remaining router after reconfiguring and unjoining. I was able to do this with different routers after unpowering the others and waiting. I repowered the routers and all showed association and I could still communicate with the first. I could not communicate with the other routers by changing the coordinator DL and at some point, lost communication with the first even after changing the coordinators DL back. I did not find DH & DL of 0 helped, although I was fooled for part of the time by a bad association LED.
I changed my Arduino code to send unsolicited data on setup in addition to responding to poll questions. I found I would see the setup message only after resetting an Arduino that was already responding to poll questions.
My conclusion is my plan will not work, but it'd be interesting to see if you get the same result if you want to try it. I'm assuming the 'complicated' API mode can be no more difficult than the 'easy' AT mode, so will try that next.