I first want to say again that I'm impressed by you! I also want to say that I'm far from an expert. I can spot small mistakes but correcting them...I'm not that intelligent to be honest.
A big thing on unracking it is to think about arching the bar out...not picking it up.
You have to keep and maintain your arch in your body. I have to think "upper abs up" if that makes any sense. It works for me in my head but if my upper abs are out and pointed upwards...my arch is there.
The rocking is bad and can be dangerous. Watch your back round. It is possible to box squat as I've described (except your knees will obviously move fwd like yours do...not really a bad thing) with a narrow stance. In fact...the guys in the video you posted are squatting at West Side Barbell Club in Columbus, OH, USA. When they do their MAX box squats...they use a stance like yours.
Keep that arch, sit back as much as you can, do NOT rock on the box, come straight back up after a 0.5 second pause at the bottom.
Man...even the most ELITE lifters in the World make lots of small technical mistakes when it comes to heavy weights. Just watch my video. I'm off center on the bar (sprained wrist, left shoulder problems), I look like my hips are dancing on the way down to the box, and my first set with 492 looked horribly off. I dropped onto the box, etc...
Gotta hit the hay big man, but I'll get you lots of info tomorrow!