Our 31-ft with no slides barely makes it in FL with 15000, so unless the 30 is insulated like a YETI Cooler, I think you're right: 13500 won't cut it.
And yes, 30A is very limiting, and a 15000 A/C is harder to deal with on 30 than the 13500 is. That said, there are very few 50A Class C's. Also, state parks and some federal sites have only 30A, so you can end up in the Thirty Amp Trap anyhow.
We can function in the hot summer sun and humidity, even with no shade, if we run the A/C all day, close blinds, and curtain the cockpit off. We can run the A/C (and converter/charger of course) plus about one other major 120-VAC draw. Not always microwave... And we heat water using LP, not the Electric feature.