Does everything work fine on commercial power? I'd make some voltage and current readings (no-load, full load) with commercial power first to establish a baseline. Then take the same readings on generator power. Then compare.
Any idea what the LRA (locked rotor amps) is for your 15k a/c unit? If it's much higher than 66-68 amps even the Champion 3100/3500 inverter generators, known for their very high inrush current capability, may have trouble starting it under the best of conditions. If your Champion is right on the edge of starting your 15k a/c, a hard-start kit may prove helpful. Of course, that's assuming it doesn't have one already installed from the factory.
