I would use both a digital and an analog volt meter on a nearby outlet to check the 120 volts.. My suspicion is you have like 126 or 127 but when you fire up the microwave it's dropping to like 124 and from there.....
Also monitor the 12 volt side of life.. I'm guessing your WFFCO has failed in the regulator stage and is passing on the higher voltage.
NOTE: if this is the case, even if the voltage on the 120 side is normal (110-120) a drop of a volt or two may be the reason the microwave makes it work.
If you have to replace the converter stage of the WFFCO.. (Which I suspect is the cause).. May I suggest a Progressive Dynamics 9200 series.
