Turns out, the reason I never considered hand washing dishes was that I didn't have the tools! No place for wet dishes to drain. No good scrub sponge or brush. No good dish soap. When the dishwasher died, I invested in all those things. I have a nice little dish drainer that sits in the second sink where the dirty dishes used to sit. I am using the dishwasher again but big items that I don't use a lot - the big bowl I mixed the muffins in, the pan I cooked the sausage in last night and some other miscellany and hand washing the smaller, more frequent stuff - my favorite rubber scrapper/spoon, plates and cutlery.
The big benefit is that the kitchen is staying very tidy which I love.