I have the Champion 3100 and it has no trouble with mine with the AC (dometic), converter, fridge, and everything but the water heater on, even in ECO mode. If the water heater is on it might trip into overload, though.
However, I've never used it at high altitude, and you didn't specify that in your post.
I usually use my generator to charge my batteries so I'd be pretty grumpy if I couldn't power everything else I wanted to run while it was on.
As far as the converter circuit, if you have a WFCO panel it takes standard QO series breakers that you can buy just about anywhere. My converter was shared with the microwave, and I wanted to be able to run the microwave off my big inverter when dry camping so I added another breaker to separate out the converter to its own switchable source.