When you say a thousand watt generator it depends on what, exactly, you mean.
I used to have (And would like to get back) a 1,000 watt portable generator that was not kidding when it said 1,000 watts (it could put out around 12-1300 peak and 1,000 all gas tank long) It powered my PDI 9180 with wizard (equal to a 9280) as long as the fuel held out.
Alas, a Honda EU-1000i can only power, as I recall a 60 amp, since it is 1000 watts PEAK, not continuous.
So is it really a thousand watt, or is it a 760 that peaks at a kilowatt.