GlueGuy, I might be wrong but I believe that the kill a watt the guy in the video is using can toggle between va and watts. He replies to a comment below where he says he is measuring watts not va.
When the voltage and current waveforms are out of phase the true power being absorbed my the load is lower that the va. This is not an appearance of lower wattage, power consumed really is lower. Reactive power (VARs) are not true power. so while you are correct that if the voltage and current waveforms are out of phase the true power (watts) reading will be lower than the VA reading, its the watts reading we want. We don't really care about va or reactive power other than it will cause some secondary heating in the inverter and microwave and the conductors between the two. BTW, modern microwaves apparently look pretty much like resistive loads, so should require very litting reactive power.
That being said, we also have the issue here that with a "modified sine wave" inverter we don't have sinusoidal waveforms anyhow. So it depends if your power meter is set up to measure only power in the primary (60Hz) frequency (like the old fashioned rotating disc electric meters are) or measures power flow in the higher harmonics. This is one reason why power companies are installing "smart" meters as fast as they can. With so many loads using switching power supplies nowadays the old disc meters "miss out" on measuring power drawn in the higher harmonics. Lost revenue for them!
I installed a 500kW grid tied PV system on a Whole Food store and couldn't at first figure out where 15% of my expected solar power output went to. Turned out the refrigeration gear in the supermarket was creating tons of higher harmonic noise which the filters in the inverter absorbed trying to clean up the line voltage waveform (PV grid tie inverters must meet ridiculously stringent specs for harmonic noise). I had a GE smart meter on the system which came initially set up to measure true power in all harmonics, so I just reprogrammed it to measure only true power in the primary frequency, problem solved!
Anyhow, all this is why I'm suggesting measuring dc current into the inverter, which is what really matters to us anyway.