It's a long standing issue with a lot of electric/electronic stuff. When W1RFI worked at the ARRL there were efforts to create a database of offenders but there's just too much stuff out on the market, and often with short production spans to really keep track. You can even have a particular make/model of something that works great, then over time the design gets changed or some part inside goes obsolete, and the newer units are terrible. It pretty much comes down to buy & try for most everything these days as the standards for EMI/RFI at HF are pretty loose, and anything coming out of china or wherever may never have been tested in the first place. Even name brand stuff, I had a DeWalt drill charger in the garage that wiped out 6M and I can hear our wash machine on 20M when it's running. Not much you can do but deal with it as it comes. For an inverter you could try basic RFI methods like bypassing and maybe an EMI filter on the output. For a while I was salvaging output filters from PC power supplies. You can get them as a component from the likes of digi-key and mouser, prolly even amazon.
Mark B.
Albuquerque, NM