My Harman Accentra draws no where near that much current. The 384W is probably for when the igniter is on/heating. During normal running the power consumption on mine is about 75-100W. You should put a watt wizard on your stove to get the exact number.
I would just use the generator you have and install a true sine wave UPS (APC Smart-UPS 750 or equivalent) between the stove and your generator. That will insure you have clean power and protect the stove from a brown out and/or dirty power from the generator.
That is a short term fix, good though. It would buy me a few hours of backup. It only provides true sinewave when on battery, so running the generator through it wont allow the generator to run the stove. But it does buy time.