I wouldn't be o sure you can't do that. You can run the A/C (one unit) on the single 20A circuit. A heat pump doesn't have any electric coils for heating, so it doesn't draw any more amps than the AC side. Just don't plan on using the microwave at the same time. Also, be sure you have a good heavy cord for it. I ran our old RV's AC in our drive on the 110V outlet for three years without any issues.
2015 Legacy SR340 360RB
2014 Jeep Wrangler Unlimited Toad
Gigi, Poppy and Sadie Lady...On the road, but not full time!