My various brand MSW inverters show mid to high 90s voltage with a regular multi-meter. So your figure indicates yours is ok, IMO. They also show funny things with the three-light tester, so don't worry about it.
MSW inverters run most things just fine. The few exceptions will be listed in their manuals. Especially watch out for electric blankets. They seem to fry with MSW according to folks on here.
We don't have anything in our rig that needs PSW, including the microwave--it runs ok, just slower than with PSW, but not enough to matter any.