Weak hand shooting is not my specialty, but I improved a lot by focusing on accuracy. I started every shooting session with a 10 round group at 25 yards: freestyle, then weak hand only and lastly strong hand only. After awhile I was able to, and still can, shoot better groups weak hand only than strong hand!! This really improved my confidence.
I also tried to handle the gun with my weak hand as often as possible, little things like grabbing the gun out of the safe with my weak hand.
You also may want to try practicing those classifiers that emphasize weak hand shooting.
Hope this helps!