Greg,
There have been a few people posting here who have switched from RH to LH in order to cure target panic. At least one person has reported that his target panic has not returned in many months (years?). Maybe he will see this and post.
Maybe switching to LH will give you a permanent, or at least a long-term cure. Maybe not. If you are left eye dominant, you should probably give it a try; it can't hurt anything. OTOH, if you are right-eye dominant, it might cause you to shoot worse than you can RH. Even then, I would say give it a try, because being able to shoot LH when you want to is a valuable thing to learn. I shoot LH a little bit just about every day, just because I think it is good for the overall health and symmetry of my body.
There is a funny thing that usually happens when someone is looking for a cure for target panic. Almost everything you try will work, for a while, because anything different that takes your mind off target panic will make it go away until you get used to whatever it was that you changed. I assume that applies to LH shooting too. I'm not saying it's not a permanent cure for some people, just that there are temporary cures for everybody. Jim Ploen once said that folding up a dollar bill and putting it in your shoe under your left heel would cure target panic....for one shot.
I think the training regimen Jim Castro wrote about above has merit. The one I wrote about in another post works for me. Jay Kidwell's and Joel Turner's methods work for many people. I have known many people with target panic, and I have never personally known anyone who couldn't lick it if they tried enough things. Maybe not permanently, but for a long time.