So are you saying that you would redo the entire litter box each day, or just scoop it clean each day until the litter box has a slight discoloration? I'm just making sure that I'm fully understanding your perspective of caring for your cat.
I've started to do the same thing with the litter out in my backyard. My dad doesn't like it and thinks that it's not compost-able, but in reality, it is. The one thing I don't do is throw the litter in the back with my cat's feces. I actually make sure to scoop out as much as I can and throw it away and then throw the kitty litter outside so that it won't stink our backyard. So yes! I like your concept of making a compost pile in the backyard as it is definitely organic and healthy.
My brother had that problem, too. He didn't touch the litter box for about a couple days more than a week? And it truly was a mess. The entire box was filled and there were little "presents" around the litter box as well. I have a cat with OCD and if his litter isn't clean, then he'll go anywhere he can.