What is causing the clothes washer GFCI to trip?
This happened to me:
Modern HE front loading washers draw a large inrush current in the pre-wash cycle as they hit peak torque when starting to spin a full and slightly wet load of clothes clumped at the bottom.

This can and does fake out certain brands of GFCI outlet, and is a well-known problem.  Because the problem isn't related to wattage, but to inrush current, high wattage resistive devices like hair dryers or small motors spinning quickly like vacuum cleaners don't trigger it.

Historically, GFCI outlets were not required or installed in laundry rooms, but in 2005 or 2007, the code changed, and they were judged to be 'wet' locations, and thus to require GFCI protection.

My solution was to replace the GFCI outlet with a non-GFCI outlet, and the washer has been working perfectly for 3 1/2 years.  But you may be able to find a less sensitive GFCI outlet, or just put a normal outlet in there and use your GFCI adapter.