That is not all that surprising to me. When refrigerator manufacturers started trying to achieve energy star ratings, the first thing they did was put a run capacitor on the compressor run windings.
My very first post on this forum, back five or six years ago was about how my 4500 watt Harbor Freight generator wouldn't start my air compressor. I needed an air compressor to build my house, so my immediate solution was to use a bigger generator. That worked pretty well, but I also built my own air compressor, out of a smaller motor, and a twin head compressor unit that ran slower, with more storage and less CFM. but it was enough for nail guns. I still use this compressor on a cheap MSW inverter rated at about 1500W and it works great!
My point is that maybe modifying that washing machine is not the best solution to your problem. Maybe it would be better to either change the generator or washing machine to accomplish your goal, which is clean clothes. Heck, it might be more cost effective, and time effective to go to the laundromat than to try and tweak that washing machine enough to get it to spin on a 1KW generator. It's fun and challenging to try and solve difficult problems, but there comes a point where whittling that square peg becomes an exercise in futility.
Just my .002
