It sounds like the inverter is using a phase timing to control the amount of power going to the charger
. You can test this by letting the inveter battery
get low enough that when you run the generator
the inverter charger
is running full cycle with phase switching early in the cycle when the voltage is low.
If that test shows the washer runs OK then it is the resonant spikes caused on the generator AC by phase switching later in the cycle.
Ferrites are unlikely to have enough capacity to make any difference and if they did, they should be on the AC supply to the inverther (the CAUSE) not trying to filter on the washer (the LOAD).
I would suggest getting a line voltage rated capacktor, like a motor
RUN capacitor (not a start capacitor) and connect that across the AC arriving inside the washer. Using the impedance of the suplly to the washer and the capcitor you would hopefully create a low pass filter that will stop the spikes that are killing your electronics
. The power factor correction it provides will probably improve generator efficiency a little too.
If you have the experience to analyze the power input to the elctronics and can find the primary DC filter capacitor, try adding another one of equal size in parallel.