I'd say the weight is simply fuc**** too heavy
Trying to lift the bar with the back is pretty common using a tough weight, like you can't really get it so your back takes it all.
More abs/posterior chain work may be good, and why not box squats ?
I think they are pretty good to push the floor hard on the ascent, pushing hard with the hips and quads.
Stupid cue, personnally on my big lifts I tended to do the same as you, but for a while I simply visualized the lift in my head while pushing and saying to myself "push with your legs, not with your back"