The run current may be fine but clearly it's the starting current that you are having trouble overcoming, after all it runs once you get it started. you're generator is acting exactly as I would expect it to if it were trying to power a load marginally over its capacity. You don't need to change the water level to change the start current, all you need is for the bearings to start to wear out or for sediment to provide additional resistance to starting or perhaps there is a starter capacitor not working optimally or corrosion in just the wrong spot or a partial obstruction in the water flow path etc.The pump is not an issue, The run current is within the published numbers, on the generator once it overcomes the start up and the pump runs without fail on the normal power. As for a low water table, I am on the East Coast Hurricane, weeks of rain.... More water than ever!
You should be measuring the inrush current at startup and compare that to a new motor (which I'm sure is impractical) Does the spec also state starting or inrush current? I bet you wish you had an old Analog meter now.
You can only throttle up so much. as soon as the electrical load (in W) exceeds the mechanical load (in hp) (figuring for efficiencies) the engine will stall. What I find odd is that it seems to recover better with more loads than without. (as far as the fridge and freezer goes, I bet if all four kicked on at one time, the multiplied start current would stall the generator. Fortunately one or more will be either idling or running but not starting when the others are starting.). Maybe with the additional resistive loads, it copes better with the inductive loads
