I run a 2800 watt generator for everything. I have a large garage style battery charger that I use for a back-up. It runs my small microwave just fine..
I own a 2000 watt inverter but only used it one time. I connected it to my battery and test drove the microwave. That thing draws ~60 amps with the microwave on! I put the inverter back in the box and run the microwave with the generator.. LOL..
I don't believe that 6 golf cart batteries will provide that much current to operate a microwave for very long. It takes a big battery to provide large current for a length of time. It may work for a minute or two but I bet the voltage will drop very fast under those conditions..
I run 8 of these connected in series-parallel and it made them grunt..
http://www.dcbattery.com/rollssurrette_s600.pdf