I know you have already answered this, but are you sure the electric side of the water heater is off? The propane side of the water heater and the electric side can be on at the same time. Might try turning off the breaker for the water heater and experiment.
For you to hear the generator suddenly rev up to the point of tripping itself, it has to be a large draw that just came on. Like a water heater (electric side), hair dryer, coffee pot, or microwave.
I can have every light and fan on in my RV, then use the pump, and my EU2000i will not change it's sound at all. Never comes out of the low rpm of econo mode.
It's amazing how well you get to know how your RV works when you boondock
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Scott and Liz - Southern NM
2012 Wildcat Sterling 32RL - w/level up (best option ever)
2007 Chevy 2500HD Duramax
Reese Fifth Airborne Sidewinder