At 700 watts the inverter is supplying approximately 5 amps. Without doing the math I typically assume that putting a decimal point before the last two numbers will give me a rough estimate. So when someone says they have a 2000 watt inverter, my mind immediately says "about 20 amps." In actuality, 2000 watts is about 16.5 amps.
Doing the calculations of what you can use is easier done when thinking "amps." In your situation, 5.8 amps is not much of a current handling capability with a 700 watt inverter. I'm in you same situation with a 650 watt inverter. Beats me why they put in such a small one. (less batteries to handle the inverter, less weight with less batteries, lass cost on an inverter, etc.,) With only two chassis batteries like I have I could only run a larger inverter for short periods of time.
Run the generator. Check your manual and you may be surprised at how little fuel it uses. I ran mine for 4 and a half days after a Hurricane and it used approximately 1/8th tank (I think) so about 10-11 gallons in my case.
For anyone else interested in figuring wattage and amerage, check out this LINK