Michmark, keep in mind there's a lot more to gauge then just the recommendation of the inverter manufacturer. Toss what they say out the window and determine your own gauge needs--1/0 might be ok for very short runs at 3000 watts but I suspect you'll want more than that.
Second, I'm not totally certain I'm following but you want to run the wires directly from the inverter to the battery. Don't go through any box.
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