I’m not sure why you need to do a 600lb. squat, because been did? And wide box squats will definitely hit your glutes harder than deadlifts. If you want a big squat, then squat big.
SLDLs definitely for hams/hip extension function.
What about snatch grip deads for overall hip development?. Do you know any cons to that lift?.
Any full dead from the floor is going to be harder on you than box squats, and probably less effective for what you trying to accomplish. Stick to various squats, rack deadlifts, RDLs, SLDLs, goodmornings, and if you feel you’re still not hitting your glutes, pick one of Brett’s exercises and knock yourself out.