When your family generally runs as a democracy, when everyone has good intentions but busy-ness and inertia get in the way, sometimes the best solution is an old-fashioned parental proclamation.
“Here’s the chore rotation for after supper clean-up.”
I guess when you don’t tell people they have to do work very often, they are pretty likely to heed you when you do.
Every night we spin the wheel one stop counterclockwise and everyone switches jobs. And almost every night the kitchen ends up spotlessly clean in the space of about ten minutes.