The inrush thing is real, but @ExFirefighter's onto something with delay start — that's genuinely what made it work for me in the motorhome.
Here's the practical bit: most modern washing machines pull 16-20A running, but that initial surge when the motor kicks in can hit 40-60A for a few seconds. With 6kW nominal solar you've got the generation sorted, but the battery needs to handle that spike without voltage sagging below what your inverter can manage.
What actually changed things for me was accepting the compromise: I run mine mid-morning when the sun's properly up and the battery's topped out. A 10kWh LiFePO4 bank (I'm running Victron LiFePO4 Smart) handles the inrush without drama, and the solar immediately starts recharging during the cycle.
The machine itself matters too — avoid the cheapest ones. Front-loaders are kinder than top-loaders. Look for eco modes that use less water and lower temperatures (less heating = less power spike).
Timing is everything though. Winter? You'll struggle unless you've got a genuinely massive battery. Summer with your 6kW array? Totally doable with 8-10kWh usable capacity.
What's your current battery size looking like?