I have a home made load bank that has enough steps that when I use the variable voltage control on the generators I can get almost complete variable load coverage from 450 watts to 15kw. It uses commercial duct heating elements.
I don't test 002s but I do test 802As. At my elevation, around 1000ft, summer conditions of 85 - 90f and humid the 802A will take about 6kw before it has response issues and any more than that it will begin to smoke a lot. At 5kw it is very happy all day long and runs with low noise and low vibration.
In the colder dryer weather the 6 kw is accepted better and it stay smoke free. But if I step a 7.5 kw load on it the unit will drop speed slowly and then trip out. The unit has an over voltage, undervoltage and over current sensing and auto trips the main interrupter relay. It will trip with under voltage and not with over load.
I have had two units at different times and tested both. They were the same. I also verified compression on both and they were good indicating a healthy engine. The first one I had the injectors tested and they were in spec. I was initially thinking the smoke at 6kw+ was indication of a problem but as it turned out the unit is just at its limit.
One word of caution regarding the load. Measure voltage and current to compute the load with a power factor of one (resistance load) to be accurate. The numbers I quote are actual. Labels on small heaters and hair dryers are often very optimistic. My 1800watt hairdryer pulls around 1350. My 1500 watt heater, around 1350 also.