This is one reason I always tell people to get the smallest generator they think they can get by with, instead of one you're 'sure' is big enough. This is especially true of military gensets, which are hugely underrated. Another way to think about it is to size the genset to your largest single load in the house that you know you will want to run, and then shed load to keep the generator in its happy range of output.
In my case, the largest single load was the downstairs heat pump (1300 sq ft floor, 5 year old pump). My MEP-002A will start it with a noticeable grunt and brief sag, and it runs at about 60% indicated load. I'm rather strict with my family about only running lights, computers and the refrigerators and freezers while the downstairs AC is on, and a lot of breakers just get left off in the panel. The result is that the set is in the 70-75% indicated load range when doing its heaviest work. That leaves us enough head room for start surges and running a single small stove burner or the microwave.
It's not a big deal to walk over to the thermostat and turn the heat pump off while doing something power intensive like making dinner. We're usually not preparing a three course banquet during a power outage anyway, so it's not a big deal. I do sometimes overcool the house by a few degrees so that I can turn the downstairs pump off for a while and use a majority of genset output for some other purpose.
The genset is completely happy with this workload, has a modest fuel consumption at this output, and wet stacking isn't an issue. If I had an MEP-003A, I'd have to run the upstairs AC as well to get anything like the same load, and I'd be scrounging load to keep it happy during mild days or winter days when we're heating with wood during an outage. I'd also be feeding it twice as much diesel fuel for the privilege which, in a crisis when there might not be diesel fuel available for purchase within half an hour's drive time (if I can drive at all), is not a trivial concern.
As for test/wet stack prevention loads, consider running a load of laundry. American style dryers are utter power suckers.