CT, this is a problem that seems to creep up every now and then, more frequently as the years go on, and perhaps you can shed some light on it
I tend to squat quite deep, at least to parallel and often quite a bit lower, nearly "ass to calves" as it were. Whenever I squat with any amount of volume (anywhere from 8x3 to 5x10 are common rep schemes I use) I am prone to getting a pain in my upper left groin/inner thigh. This isnt soreness, this is "If I bend this leg the muscle will snap in half" kind of pain.
I suppose the easy answer is just not to squat so deep, or switch out to something like the trap bar dead lift, but for things like challenge sets and volume I really like the squat (which I now use an SSB bar for) and feel its a great exercise for me.
Would something like your Body Builder Box Squat ( https://www.T-Nation.com/training/box-squat-for-bodybuilders ) be suitable for any amount of volume if not done in the style you describe here, but more of a traditional constant-tension style?