Knowing it's conclusively the inverter is 90% of the battle. There's only so many points of noise egress there can be. Depending on the kind of interference will require different mitigation. Could be conducted, radiated, or both. The trick to taming interference like this is first characterize the noise - note the bands/frequencies the interference is present and corresponding S meter levels with your standard antenna setup. Then try something, like putting ferrites on the input and output leads. Re-assess the noise again - better or worse, maybe just some bands and not others? Or maybe no effect at all? Any result, including no result, is a clue as to what the interference is and what to do about it. Depending on the dollar value of this unit (any more inverters aren't very expensive) it might be time/effort ahead to just replace it, betting that a "better" one will have reduced emissions (may not...). So you start with a band/level noise survey and spend some quality time with ferrites, caps, chokes and EMI filters and noting cause/effect. With any luck it's not coming straight out of the plastic inverter housing and into your antenna, and standard I/O mitigation techniques tame it down. Another point to address is common mode. If your antenna/feedline isn't isolated, then even small amounts of interference can couple efficiently into your radio via the coax. So improving isolation there can also help reduce noise.
Mark K5LXP
Albuquerque, NM