The shiny black thing near the top of this photo with two posts with red wires attached to them is the replacement Klixon CDLA-80 circuit breaker. Unlike the one Lisa removed, this one does not rattle when you shake it, which is a good sign. The red wires are, at right, the feed from the coach battery and at left, the line that runs through the body of the RV back to the circuit board with the fuses that power all of the "hotel" functions like the water pump, interior lights, and most importantly to me, the DC accessory plug that powers the CPAP.
I hefted the deep-cycle RV battery back into the bay and Lisa connected everything. The good thing about this replacement is that it's the same circuit breaker from the same manufacturer, not a "replaces OEM part" or other compromise.
The replacement took only a few minutes, and everything works as it should now. Given that it's starting to look like I'll need to make another trip to the Bay Area in the next few weeks, this is a good thing. But fortunately that week is not now, because I don't want to have to buck snow, ice, and chain controls on I-80.