If you can hit, a few shots to the body should make him a little less enthusiastic about moving around. Also, regardless of what stance he's in the body is your only consistent target.
I switch my styles alot! i mainly box southpaw but i am as good which ever way i fight. The problem is.. you can get in close and try to rush when you see the switch but if its me i would not be switching when your not in range and the switch will take 1 second to do so your have to be bloody quick to catch him. But strait right as fast as you can.