I've seen them near a 3500 watt load with out any issues. I may not be understanding what you mean, is induction load different?
It is different but the real issue is having a gauge that is calibrated for a power factor of 0.8 and how that will under report load for a resistive setup.
One of the things I recommend here is to leave the electronic governor alone and run on the mechanical governor until you have the unit making full power without bogging down. You're adding too many variables into the mix.
When you load the unit up you need to take the voltage and current readings and make sure you haven't overloaded it. Sure there are units that will take 3.5kw of load. There are some that won't. Lets find out where yours stands mechanically engine output wise. Depending on its life before you it is quite possible you have some carbon built up around the rings and its robbing you of some compression and as a result engine output power is not up to spec. That can cause black smoke and reduced power. If it won't run at least 3kw for hours and hours on the mechanical governor without bogging down then you still have a mechanical problem. Don't trust the gauges on the machine. Verify your 3kw with your voltage and amp meters.
Altitude absolutely can play a part here. At 3000' MSL you will be about 10% down on power versus 0' MSL.
You've done a lot of good work on the machine. We need to run the engine problems fully to ground before moving on. Strictly my opinion.