I have a similar setup: 31ft, one AC unit, and we've been to the desert in the summer, and it works fine. I agree with Fl gypsy: Keep the fan on hi, and always on, and don't close those vent slats directly below it. Yes, there will be less air going through the ducts, but it won't freeze that way. Freezing seems to happen when you have less air moving across the coils, which doesn't warm the refrigerant enough for the next cycle. My buddy in the HVAC business says it can also be a sign of low refrigerant, but only if you're not blocking or reducing air flow.
One thing a single AC unit won't do great, is to suddenly drop the temp of the entire coach. Get those little pillows for the roof vents that insulate, close the shades on the sunny side, and open all the ducts and the bottom vents, it'll work fine. Vegas was 109 while we there, and yes, I know it can get hotter, but we were comfortable inside!
BTW, our dash air can freeze if I turn down the fan on it, too. I just switch it to vent, and when the temp starts to noticeably increase, the ice has melted, and back on it goes, with a mental note to keep the fan on a higher setting. I like dehumidifiers too, but they give a net increase in temperature to the interior while giving a drier humidity.
Coachmen Pursuit 31BDP 2013, 300w solar, 1200w sine inverter, In-motion Winegard Dome sat. ant., L.E.D. lights, P2 brake controller, Yamaha 250 on back carrier, or pulling Stehl dolly with Hyundai Santa Fe