when my girlfriend was learning to squat, i made her do a zillion bodyweight squats with a broomstick. I also got a stool that was just below parallel for her and had her just squat, when her booty touches the stool she comes up... then EVENTUALLY we started using a 20lbs bar.
sounds like you are leaning forward an awful lot. i notice when i see people attempt pistols, they have a lot of trouble getting to the bottom position... same kind of problem. the solution is to START from the bottom position.. and after a while it becomes comfortable.
id say do the same thing. sit your ass down on the floor.. use your hands to get yourself into the bottom position of the squat. stay there for a while.. get used to it, because thats where you wanna be. then stand up without using your hands. the way you stand up should be the way you drop to squat position, roughly. i can't imagine that you have so much tightness that you can't squat... i don't believe it. your body just doesn't quite understand the posture and mechanics of the squat just yet. watch BUNCH of videos on squatting, thatll help. look up rippetoe.