I think you pretty much answered the question yourself.

If missing ROM in Squat, I’d say box squats would be pretty good for you. If you feel your hammy isn’t what it used to be, then do some lighter DL or Straight-legged DL with one leg or so to make sure you strengthen both sides equally.
Weak rotator cuffs? Then do some external rotation exercises and start working on your pressing etc. Keep focus on light weights and work on your form and I guess everything will solve itself.

That’s at least what I would do, not saying its right or anything, but thats what I would try to do with your problems.

Regarding squatting, try to do the 10min paleochair every now and then. I should probably do it more often my self, but its so hard to sit there for 10 min..

Good luck.