I don't follow the logic.
What's wrong with just using a transformer of one type or another to step the low line voltage back up into the range that the microwave oven is specced to work in?
As in using a basic buck/boost autotransformer to bring your 90 - 100 VAC back up to the 110 - 130 VAC that the unit needs to work properly?
Why all the unnecessary run around when a basic multimeter to figure out what input to output winding ratios are needed is more than sufficient?
Which BTW, a common 120:16/32 buck-boost transformer configured as a boosting auto transformer would give you two voltage boosting points to work with as your primary line voltage drops by simply stacking the two 16 volt windings in series on top of the primary winding thus allowing you to boost 100 - 110 VAC to 113 - 125 volts at the midpoint tap and 87 - 100 VAC to 110 - 125 volts at the end point tap.
Also being the transformer only has to handle the current at the step up voltage difference a 500 VA unit would easily handle a 1500 watt load all day without issue even at the lowest 87-volt input level.
120/240:16/32 volt 500 VA transformers can be found all over the place for around ~$80 - $100 online. Or you can make your own out of an old 15 - 20 amp rated battery charger transformer too by stacking the secondary windings in series with the primary.