The solution here is inverter drive appliances. I had a cheapo but great thrift store inverter microwave. My cheapo junk 3000w inverter could run it off a few hundred Ah of batteries without issue, still spitting out clean power on the other outlets. A regular microwave(with a lower run wattage in theory, by about 1/3rd) would instantly blow the thing up and set off its obnoxious alarm.

With some carefully selected appliances you would probably be fine. This stuff used to be super pricey, but now even the cheaper brands are putting out inverter drive ACs for example. Not window units, but mini splits and home systems