Lisa opened the propane bottle and confirmed that gas was flowing by lighting the burners on the stove. After some coaxing, the furnace lit off, and eventually we also got the water heater running. We also plugged the RV into shore power so there was no question of running the furnace fans all day if necessary.
After an hour or two, the RV heated up enough that the water lines started to thaw out and water began to run again. The hot water from the heater came through quite nicely once the faucets thawed sufficiently to let it through. We speculate that except for some bits at the water faucet, the system didn't freeze solid, but turned to slush, and that plugged up the water pump until the furnace got the place warm enough to let water flow again.
We bought eight more gallons of RV antifreeze. When the hot and cold water both flowed freely pink (showing that the solution had permeated the lines), we shut the furnace down, but left the water heater running. I'll turn it off before leaving tomorrow.
This was something of a near miss inasmuch as if we hadn't got after this right after the weather hit the sub -10° range it might have caused a line to rupture, or worse, burst the water heater. As it was, it was only an inconvenience.
I've been packing things into the Rolling Stone this evening in anticipation of an early start tomorrow. The RV dealership won't be able to get work on reinstalling the steering stabilizer until I get back from this trip, so I'll need to take things pretty carefully (and probably slowly, to the dismay of other motorists on I-80) tomorrow.
*Recap for those who missed it before: there is a form of antifreeze (usually dyed red) intended for fresh-water systems like RVs and boats. It's non-toxic, but you don't really want to drink it. It won't kill you, but it will probably make you sick. This is not the same kind of antifreeze you put in the radiator of your car, which will poison you if you drink it. I don't generally drink the water in the fresh-water tanks (I have some bottled water), and only use the water for sanitary reasons, so this is not a problem on board.