This is a problem I've read about with newer washing machines. They have what is basically a three phase motor and thus need electronics that run it. The non-linear draw causes the inverter waveform to go lopsided and then the washer throws an error.
If you can, just for experimental purposes, run a bench grinder on the same circuit while starting the washer. I've had success with this method starting difficult loads on an inverter before. The grinder acts like a flywheel to smooth things out.