The only catch is that, while the browser can always find the MythWeb service, sometimes MythWeb cannot talk to the MythTV back end. I have no idea why the connection works some times and fails other times. Sorting that out is for another day. Fortunately, the problem is easily fixed using shell access, since SSH is enabled (by default, I believe).
For future reference (since I will forget them, probably within the next hour), here are the only commands I seem to need in the SSH shell. These may be somewhat specific to Mythbuntu, so anyone using a different version of MythTV be warned: Your Mileage May Vary.
- sudo service mythtv-backend [start | stop | restart] to start/stop/restart the back end (when it gives MythWeb the cold shoulder);
- sudo mythshutdown --shutdown to shut down the server remotely after I'm done playing with it.