I was reminded over the summer (rather embarassingly) just exactly how much power 600 watts is when two 5 light fixtures in my basement with 60 watt bulbs that I’d mindlessly wired up in my basement caused an outlet in my shop (wired in series with those lights) melted down while my wife and I were cleaning. Trust me, 770 watts isn’t much more.
For about the same price, you could get 5 times that power at Costco.
And for roughly double the price you can get 3 times more power than that.
And with the some help from a real electrician you can tie it into the house when the power’s out (NOTE: you HAVE to disconnect from the utility, not merely plug in and run it while the power’s out).
That’s what I’d do. And keep a few 5 gallon gas cans in the shed.