Def work hard on the hips like other have said. If you can't leg press, keep working front squats and hammering single leg type stuff. Anything will help, but I personally like the "fake" single leg stuff like lunges and RLESS. Get some bands from eliteFTS and squat using those +weight, that will hammer your legs/hips pretty good.
Also, it sounds like you may be able to bring up your obliques more and hit mobility work. Those are pretty common issues for ppl falling forward, aside from weak backs. Hit those well, too, the oblique really stabilize in that bottom position of the deads/squats.