A 1000w inverter can be expected to draw 100a from the battery with a 1000w load on the inverter. Since the inverter will run a toaster or a kettle at 90a draw just fine, even though it is for short times, you are likely to do just that :) IMO don't even think of using #6 instead of #4.
---I don't understand ampacity amounts for different gauge wires since they don't say (or I missed that) how long the wire is. AFAIK if the wire is shorter it can do more amps at the same gauge.
That is why you can use short pigtails of thin wire to go from small terminals to fatter wire that won't fit on those terminals and it works ok--the short thin wire is not a high R bottleneck for amps.
Can somebody please clarify what those ampacity tables use for their wire lengths? Thanks.