Just to follow up:
The place in town (Pikes Peak RV) did indeed have the part I needed in stock, and it was apparently, in the shopkeeper's words, "the last remaining one in the world". I started to do it myself and then remembered how bad I am at sealing things on correctly so I had my mechanic do it since he was already working on the furnace anyways. So it's as good as new now. Furnace is working great too finally! Just needed a new thermostat. I'm ready for my first ever pre-winter trip now. Should be fun.