mortdooly,
I have found that shooting position is more important than strong hand versus weak hand. Several years ago I was at a USPSA match and grumbled when we came to the one stage that always shows up that requires weak hand shooting. A seasoned shooter told me that this is why you always include a portion of your practice time shooting with the weak hand only.
Two things I took away from Mike Seeklander's portion were:
1. I must include weak hand shooting, unorthodox positions, and gun transfer techniques in every practice session;
2. I must be aware of how I set up my practices to mimic the situation I am practicing for - In the car practice I would have put a barrier right in front of me to limit my freedom of movement, and I would have moved the side threat targets more to my rear to better simulate a person in the passenger seat or that approached along side from the rear.
My point, in much shorter form, is, careful and regular practice is the most important item.