Great advice from all on dealing with wind and casting. Over time I have extracted close to a dozen flies from fishermen. A couple were large flies in the cheek and neck. I've seen a few rods get beaned with heavy clousers and go "bang" on the next cast. If you fish on the Cape long enough, the wind will be on your casting shoulder at least 50 per cent of the time.
As Juro and others have said, backcasting is a tried and proven method to thwart the wind. The one downside to this method is when you are sightfishing. Most will take their eyes off the fish when turning their body to backcast.
As someone with average eye-hand coordination, I started practicing flycasting with my other hand about five years ago. The first step was attempting to form a short, tight loop by emulating what I did with the other hand. I was dismal at the beginning, but as I continued 15-20 minute sessions daily, muscle memory kicked in. Once I felt confident casting short distances, I started lengthening the line, and then shooting on the back and forward cast. The next step was accuracy, and finally learning the double haul. The double haul is not hard if it is broken into single hauls, and then combining them.
Learning to cast with the off-hand has actually improved my casting with the other hand. It has shown me some of the poor techniques I have developed over years of bad practice.
CSJ60 is another guy I fish with that has become an excellent caster with his off-hand.
If you feel overwhelmed by learning to cast with the off-hand, don't. Trust me, if I can do it, anyone can