[rickst29]

The WildKat, a slightly modified PD converter "main board assembly", cannot be programmed to limit either it's input or output current to a value below its design limits. It will always try to "dish out" whatever the battery string (ansd other 12v loads) are willing to absorb, up to a limit of about 60A. I measured the maximum continuos capability of my own unit at 63A during an initial test when it first arrived.

However, the continuous input draw required to provide 60A output @ 14.2 volts is only about 1070 watts. (60A * 14.2 volts = 852 watts, with internal power losses at 80% efficiency increasing input power rating to about 1065 watts.)

But your Victron shows only 389 watts delivered at 14.26 volts (27.3A), shortly before even the "2000 watt" generator bails out with an overload error. That continuous output power rate SHOULD be pulling only about 500 watts (continuous) from the input 120-VAC side. The WildKat can pull much higher current to charge internal capacitors for a short period of time, but that that won't take very long. But I don't know the capacitor sizes and the maximum current which could be drawn, so this is a SWAG.
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If the 120-VAC wiring between the generators and the WildKat is all in excellent condition, without short circuits leaking power away and also with no high-resistance problems at connectors or the circuit breaker, then the problem will be internal to the WildKat - most likely a failed capacitor.

But the WildKat 120-VAC input "hot" wire SHOULD BE on a circuit breaker limited to 20A (or, even better, just 15A): Your "27A" input current measurement should have tripped the breaker, if it continued for even a single second of duration. Because the breaker did not trip, AND because power from the rI suspect 2/3 of the measured input amperage is being lost in a ground fault, before reaching the WildKat.

Can charging run for more than a few second from the 30A cord with a household/grid connection? That test can be performed on a 20A circuit, but it should be on a standard breaker - not a GFCI.
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You could also reduce the maximum output power delivery of the WildKat by changing the battery type DIP switch to "GEL" (that switch position is also used for AGM batteries), enforcing a maximum output voltage limit of 14.0 volts (instead of allowing more than 14.2, as indicated in your 3rd picture). But that change would only be effective for "power limiting" when the WildKat was delivering nearly 60 Amps, and you're nowhere near that level of current.