What do you do with straps and box? I do them at the end of a wall (doorframe without a door) while hanging on with both hands. The supporting foot is at the wall end. The extended leg goes along one side of the wall. It allows me to engage the right muscles and manage my form but I know it's cheating!
They're super hard, I really struggle with balance and not going on to my toes (which puts dangerous pressure on your knees) once you get deep in the squat. You're right though, can really see the value in them - great for ankle and quad strength.
Very different methods of working on it. The straps aren't that different from what I do by hanging onto the edge of the doorframe. I guess an advantage of that approach is that you can control your alignment and work your glute/hamstring harder. With the box, you aren't going down as far but you need to work hard to manage your own stability so you're on the road to doing a proper pistol squat. Interesting!