Well, now that I've got it working in the Program modes, I'd rather not mess with that by trying to learn dip-switch changes. Otherwise, I could have another uncomfortable cold night while I try to wake up enough to debug a complicated thermostat!
The only times that I've successfully gotten the thermostat to change what it is doing the by having the words "Program" flashing. In particular, I've never been able to simply push the up or down arrows to increase or lower the temperature, which I can easily do on my home thermostat.
I think that the problems seem to stem from the Dometic being a very powerful thermostat that can be made to function in many different ways. As a result, their documentation doesn't do a good job of explaining how to make the thermostat work, because the operation seems to depend so much on the dipswitch settings.
Thanks to everyone for their advice and help.