I'm a little late on the box squat thing.
But I'd stop bouncing around before my reps, sit back further, and also change the box so that the corner is between your legs. That way you don't have to worry about missing the box, it becomes impossible.
Watch some Louie Simmons videos if you want to know how to box squat.
But if you aren't competing in gear, and want to be strong, just learn how to do a regular squat.
If you want to use less weight, and make that harder, do pause squats. You can concentrate on your positioning in the hole like you're wanting to do, and light weight gets really heavy when you sit in the bottom for a few seconds.
If you want to squat more weight, squat more, squat often, etc. "5x5 and eat more" was the advice given to me by people who are much stronger than I am. I got strong when I listened.