There are two big problems. Both are weaknesses/technique problems. Your upper back is not staying tight enough. This is where I fail as well when I miss a squat. The BEST exercise I have found for this is seated upper back good mornings. Will they help you? I have no idea. I do know that Working the hell out of these has put about 50lbs on my squat.
Also, your abs are either weak or not staying tight enough. Drop whatever ab work you are doing and start training with some heavy weights in some, i hate to say it, sport-specific positions. Front squat holds work well, so do suit case deadlifts.
I don't think GMs and GHRs are good for upper back strength. If you are losing tightness there when you squat, there is no way in hell you are in a good position during a gm.