Right/Left Strength & Coordination Discrepencies

I have been using KBs for about a month and doing the Program Minimum with 16KG. In addition, I am practicing some C&Ps, High Pulls and Snatches on my off-days with 12KG to learn the coordination.

I have noticed that I have significant differences in both strength and coordination in my non-dominant (Left) arm. For example, I can press strongly and with good form on my right side and can only manage a couple awkward reps with my left side. I can clean the 16KG smoothly and with good form on the right and press it smoothly, but the left side seems to require much more effort and still looks and feels so much more awkward. On the snatch, my left side does not seem to have the ability to punch through at the top. I feel that my elbow on the left side is the limiting factor. In the past, I have always done DB bench press instead of BB bench because it would aggravate my elbow. It would not cause pain, but felt like a tendon sort of popping back and forth over the bone in my elbow with heavy loads. Doctor just suggest ice and performing exercises that do not cause this phenomena.

I have had my form checked by an RKC, so I am assuming this is a strength issue and not bad technique. My question is what is the best way to solve this discrepency? Should I perform more reps on the left side to balance my strength levels or should I perform traditional (non-KB) exercises to target and specifically strengthen the left side?

Any insight would be greatly appreciated