I agree with riccilOve,
My horse is an OTTB as well. In my experience with off track horses many of them like to travel on the forehand. Many of them also have more trouble one direction than the other. The first place I always start is lounge work. Getting the horse to use their body and carry their body in a differnt fashion.
When the horse is using his hind end more his topline becomes more rounded sort of if it was a hump back...as one trainer explained it to me.
The horse will learn to use his/her abdominal muscles as well.
A cross canter is very bouncy! When your working with this horse it is important to work on the walk and trot first before procedding to the canter. Just as ricci has mentioned.