Have your head move the same way your lead foot is. Keep your left hand tight, and circle while jabbing.
Here is something. Slip the right hand by bowing forward so the right just grazes the top of your head and your weight is on your front foot. Then instantly come up with a short left hook to the head. This worked for me. And usually his right hand drops when he is bring it back leaving his face wide open for a left hook counter. Keep everything real short. Timing and practice.
Maybe try to keep the left hand a bit higher? That should make most punches land at your guard if you freeze and don't move.
Spar southpaws a bit, defending the southpaw jab could help you deal with the orthodox right hand better.