My jerk is no stronger than yours so don't take what I say as fact, but I know that my jerk improved when:
1. I did it more, including jerks from the behind the neck as supplemental exercise
2. More shoulder pressing and push pressing, moreso of strict pressing.
Thats what helped me. I still miss jerks sometimes of course.
I guess my jerk is stronger because I weigh less, but I would wait for some f the more experienced guys to speak before doing anything drastic with you training.