"Most AC motors will run on MSW inverters with an efficiency reduction of about 20% due to the harmonic content." If you do not boondock... hooked to shore power most of the time, keep what you have, but I would add a transfer switch so it is running on shore power when you are hooked up.
I went with a 1000W PSW inverter (500W would do it) because we do boondock often. Our 21 cuft refer runs at 100W and takes 4-5 times that to start. The extra power is used to power a Sat dish, DVR/receiver, and TV so it will record saved programs.
If you decide to do something, I would probably just add a PSW inverter to increase your power to 1500-2000W.