Your model number makes it a 13500-BTU unit. There was also an 11000-BTU Penguin which presumably would cost a little less. By that I mean "Less Expensive" - We're talking "RV" here, about as bad as talking "Boat" or "Pool."
The hole just about all of them mount on is 14 x 14 inches so in that sense they're all interchangeable. BUT...
...and it's a BIG BUT... RV A/C units are now being sold almost exclusively as individual Upper and Lower components. IF IF IF your Upper is "BAD" (and I'll get to that in a minute) then the least expensive solution is most likely another Penguin Upper. Just hope that Dometic hasn't superseded your design to where the current version of Upper isn't compatible with your older version of Lower.
"BAD" to me, in an RV A/C Upper Unit is a Failed Compressor --OR-- coils leaking refrigerant. Compressor and Coils are the Hermetically Sealed (hence "HERM" on the Run Capacitor for Compressor). Anything less than the sealed system (fan motor, fan blade, capacitor(s), controls) I would attempt to repair or replace.
Yes, your existing thermostat should still be able to control the Furnace. Sometimes a residential thermostat from Big Box or Walmart can be used with very good results at a very minimal cost.
You have a two-way RUN Capacitor. It is in fact possible for ONE "side" of it to go bad and the other side still run its component. At home, I have had the HERM side go bad (no compressor running) and FAN still good. I have also had the opposite. Come home to an overheated compressor because the FAN side of the capacitor had failed.
The BLACK capacitor you describe is Start Assist. WITH POWER OFF, Yes, you could short the terminals without burning anything, then disconnect them and see if it would start with just the HERM side of the capacitor. The Assist is for when supply power degrades, like low campground voltage, using a generator, or perhaps very high outdoor temperature. But Compressor will NOT run if HERM is bad.
$55 to troubleshoot is probably a half hour at the dealer's labor rate, not at all unfair. If you want to take his estimate under consideration and discuss it here, feel free.
If you feel uneasy about getting up there, into it, around electricity, then please follow your gut and have somebody else do it. I'd help if we were closer. Nothing on that RV is worth risking life/limb. I fervently believe that. I just need to work on following it...
