In one of his articles, CT discusses the benefits of ATG over parallel. He convinced me, so I was doing ATG with ever increasing weight, but then a Sports Doctor I went to see to discuss an ongoing Hammy and clicking knee problem said go to parallel only as ATG is bad for the knees.... Sigh. Makes it hard to know right from left (let alone right from wrong!). :-/
Have you tried wide stance (SUMO-style squats, to whatever depth; or deadlifts? I can feel a difference in my back (especially), knees and hams when I change the stance. Maybe worth a shot?
Your suggestion of box squats is good too - and changing the amount of time you sit-down is also a good twist, as you can completely eliminate elastic energy if you wait for a few seconds. It makes it go from hard to bloody hard.