I fought OTT for years. Even when I thought I stopped, I'd check video and there it was. I have recently FINALLY stopped doing it after several lessons and a very concerted effort to stop it.
Here are the things I did. First, check your setip and make sure that you are not standing closed to the target. That was my first problem and I see it every time I go to the range.
Secondly, the first few inches of the downswing are the most important (for me, at least) in preventing the OTT move. The very first move from the top of the swing for me was OTT (in other words, the club head moved toward the way my feet pointed at setup), so I slowed that move down tremendously. I took practice swings where the first move of the clubhead from that position was to drop (down toward the ground AND behind me) an inch or two. Once that club moves down, it's harder to go OTT. This takes a lot of time and patience on the range (and a video camera).
Thirdly, I drove the rear elbow (left elbow for me because I'm a lefty) as far as I could toward my right hip on the downswing which REALLY makes the club drop to start the downswing. [Sidenote: if you're a single plane guy, the is not a move I'd recommend]
Finally, similar to the thought raised above about keeping the back to the target, I swing at the ball as if I want to hit it 45* to left field (again, I'm a lefty). After several months of doing these things - and terrible contact with the ball - it started to click. First, I stopped the OTT. Next, I started to hit the ball more solidly. Now I'm getting a nice little draw. Hope this helps. Good luck!