The only snag I hit was when I was changing the network ID away from the default.
That's indeed what seemed to be the case: reloading the settings worked fine for the ground radio, but the air radio couldn't be contacted.
At this stage I could have tried resetting the ground radio back to network 25. That would have been the easiest thing to try, and would have worked fine to get the radios talking.
But I had noticed that the air radio pins were a standard FTDI connection, so I had another thought. Perhaps I could connect the air radio to the computer via an FTDI adapter, and set it to network 26 that way. I have the industry standard sparkfun FTDI adapter, so I gave it a try.
I ran the APM Planner again, and everything worked like a charm. I could read (and set!) the air radio settings, and connecting the APM in the APM planner worked as expected.
(toc: 3DR Radio)