To clarify, the inverter runs up to 1000w continuous according to its spec sheet, unlike the similar Prowatt 1000w PSW which ISTR is 900.
Mine only fried when I ran it at 1050w, with its overload light on, too many times ("too many" is defined as the number of times run when it fries a circuit board part)
The #6 and 60a should be safe, but I agree it could lead to low voltage alarms and shut downs sometimes. Just have to try it out.
To stay above 11v loaded, it is best to have fat wires and a big battery bank. With just two batteries, you have little margin to run the loads when the batteries are near 50% before you start the inverter. Having fat wires with just two batteries gives you more margin.
It was shown on here a while back that AGMs can take a big load and stay above 11v much better than Wets can. If you have a small rig that cannot carry more than two batteries, and you want to run big inverter loads, having AGMs would be the way to go.
This all matters to an early riser making his morning toast with his batteries low--to be recharged later in the day once "generator hours" open.