The only thing not suggested yet, and it may not matter, but the Firman uses a frame bonded neutral. You did not mention if that was disconnected for use with the house service. I assume it was not. If you are using a basic inlet connection box and interlock or a non neutral switching transfer switch, then when on the Generator you have two paths for neutral current to take. The normal neutral but also the ground which is not supposed to have any current on it. There should only be one place where Neutral ties to ground and that is in the house main service panel.
My setup here is an unbonded Westinghouse 9500DF <23% THD through a 50 amp inlet box and a Reliance Controls transfer switch. I have a 3 ton Coleman (YORK) two stage AC fitted with a soft start kit. It is not a variable speed inverter type though. My 9500 running watts (7500W de rated for fuel and altitude) powers everything thing connected via the transfer swtich without issue. This includes the AC, Refrigerator, computers, QLED flat screen, microwave, smart home devices, LED light bulbs, smart dimmers (@ 60Hz or below), cable modem and wireless access points. I do have UPS on things I don't want dropping out and I have a whole house surge suppressor in the main panel, a surge supressor installed across the inlet box at the transfer switch, and another one installed at the HVAC air handler in the attic. Everything is working off the dirty power 9500DF and others report their dirty power gensets are working for them too. Try ruling out the bonded neutral either by disconnecting it at the generator or by using a neutral switching transfer switch. Tip: You can make up a bonding plug (a plug with ground and neutral shorted together) for your Firman to use when it is not neutral bonded by virtue of being connected to the house.