I was thinking that I started doing ATG squats about 8 months ago and had to take 50 Lbs. off the bar to go deep but maybe I should do parallel or box squats with more weight sometimes to hit the quads.
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.
The sports doctor is wrong. It’s much more likely an issue of flexibility or weakness of the VMO. Try doing Peterson step-ups or banded terminal knee extensions plus paying close attention to the subtle nuances of stretching for about a month and seeing if the clicking doesn’t go away.