I think that some of the inverters installed on Cutwaters were Modified sine wave. If your inverter is a modified sine wave inverter here is an explanation of why the voltage is lower. Many less expensive volt meters simply take the peak voltage and divide by the sqrt of 2... For a sine wave, this is exactly correct for calculating the Root Mean Square (RMS) value of a sine wave (basically, the 120 VDC voltage equivalent work of a 170 Volt Peak Sine Wave).However, a MSW (Modified Sine Wave) inverter outputs, basically, a square wave. The peak of the square wave is much less than 170 volts. So, the inexpensive meter reads the peak voltage, applies the sine wave conversion factor, and comes up with a low RMS reading. This is basically explaining that the 80 volt reading is because of the volt meter is not capable of reading a modified sine wave inverter voltage correctly.
The 1500W inverter should be able to operate the microwave. The information you gave is vague , Do you have the main breaker on at the Ac panel? Do you have the microwave breaker on at the main Ac panel? Does the microwave work ok when on shore power then when you switch to inverter it does not?