I agree that it's a flexibility issue. I'm convinced that I am the most inflexible guy on the planet; I can't touch my toes, but I can do overhead squats. Go figure. Back when I was really into training the Olympic lifts, I knew that I needed to work on flexibility.
I never developed flexibility in my wrists - that's still a work in progress - but I did get fairly flexible in the lower body. Start with the ankles - before each workout, I would get on a step, do several reps of one-legged calf raises, then stretched out the calf. I did this 2-3 times each leg. Then I would go squat. No boards or plates under my heels. Go low. After a few reps, it became easier -- the weight on the bar would push me down and provided the needed amount of stretching.
Same thing when I tried OHS. Make sure your shoulders are good and warmed up. Start with the bar and keep adding weight. I found that it's actually easier to OHS with some weight on the bar than just with the bar itself. Again, the weight will stretch you out. At least this is what worked in my case. Everyone is different. I for one hate doing stretching exercises; I get my stretching done from lifting in a full ROM, if that makes any sense.