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120v @60A should be 7.2kW

That would put your 802a at 115% load, a tad high but nothing the generator can't handle. Wouldn't the load go down as the batteries charge? If it does I'd say you're golden.

Do you know the maximum charging rate on that inverter/charger? (How many amps it can take at 120v or 240v) If you're just charging batteries I find it unlikely you'll need more than an 802a. Keep in mind at the same load the 803a will burn roughly double the fuel of an 802a, if you're...