Thanks for the tip - I'll add it to my notes.
I did remove the wood panel in front of the furnace and blow the area out, and managed to see a label with the number "35436", which makes me think the model it's probably a Dometic (Atwood) DFMD35.
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I do have a lifetime warranty from the dealership, but I believe I'm supposed to have it inspected once a year within 30 days of the anniversary date, and that's coming up in ten days on Dec 23. So now I'm not sure which to try scheduling first - inspection or furnace repair.
Also, the first shop I called said they're backed up for the next six weeks, and the second wanted me to bring the RV to them - and I don't own a tow vehicle.
Man, this is a stressful situation. Maybe I bit off more than I can chew.