The answer is simple, work this in reverse. Cook for one and wash for one and pick a space that is yours and only use it. E.g. have a second bathroom, use it exclusively.
Then make the change, and don’t say anything and spend the residual time on you.
I cook awfully even at my best, but I do all the dishes and laundry without a fault. We don’t have kids (we have a horse farm) on every day off I help with the stall cleaning so she doesn’t have to.
When I have the full energy and time, I will even do a full house cleaning of the floors. The only problem is I am not as good as it as she likes, so I get the fun tongue lashing of why can’t you do better. So I try and just realize there are things I need to do better.
He needs to do this if he considers himself a feminist and most importantly a good friend, lover and husband … otherwise it is all talk and no show.
Before other guys might say WTF …. my libido has always been higher then my partners (though with a fun twist of irony as we both age the roles are starting to switch :) ) so while I have my household and farm maintenance required, she has her intimacy targets … (now … this is obviously consent driven).
Life and relationships take two to tango …. whether it is in the sheets, with the mop, vacuum, or dishes ….