I was seriously considering switching to RecPro 9.5k from my 11k. Since 11k just handles 100° high humidity, I'm reconsidering.
If you check RecPro specs, 9.5 and 13.5 have very similar power requirements.
Unless you have shore power, heat pump, probably wouldn't be worth it. Running generator to run heat pump, would use more fuel, than just using propane furnace.
What I would recommend, watch for take off AC that someone upgraded. For my old camper, I got barely used 13.5 coleman unit for $200. It started and ran fine, on 2,200i Honda. I use premium ethanol free gas, it makes difference in power.
15k won't run on generator without soft start.