We always used a MSW inverter for MW with no troubles. Check the back of the MW for its real 120v input watts requirement and then get the inverter that will do that.
Eg, a "700w" Danby wants 1050w input. A "1000w" might want 1500w input. AND the inverter has a continuous rating that is less than its "name" so eg, a "400w" will run 320W and a big "2000w" will run something less. So check both actual spec figures for matching them.
It is true the MSW will take longer to heat something up than a PSW, but it is hard to notice in real life. EG your spud is done when you can stick a knife in it, but when is that exactly?
You need enough battery to run the MW from the big inverter even with MSW. Follow the installation instructions for the inverter wiring gauge and fuse once you choose the inverter.
