This will sound funny, but maybe try no support at all?
I've had both problems, and recently - on a suggestion - started using Puma's for my workouts (I don't run in them). But for everything else, I've switched to them. There is something about the artificial support in tennis shoes that can sometimes cause your foot to overcorrect and actually exacerbate the problems.
I use the Puma tapers, which is basically just a soft shoe with a rubber sole. It's the closest thing to going barefoot that I can find, but it still provides traction on the floor. In my experience, allowing my foot to take it's natural motion, rather than trying to support the arches and ankles has worked miracles.
I have not had a problem with my knees, ankles or feet since making this change a few months ago.
Just a thought that's probably a little different than what you had in mind.