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I just posted a similar question the difference being that you must have quite a bit of skill.
It's got to be a mental problem. You have a great swing to be capable of such low scores. Call me "Mr. Obvious", but are you ok with giving up distance on your drives to keep it on the fairway or is that bad advice? To me and my limited knowledge of the game, its a no-brainer. I don't give up that much yardage and it beats the heck out of penalty strokes.
I have been working on stopping my backswing at the top when I practice - trying to get my brain to memorize the stopping point and the beginning of my downswing. Again - I'm the last person on the forum who should give advice.
BTW... I can swing left or right side dominant with nearly the same results. Left side generally tends to be more consistent for me.
I have a similar issue, speeding up during play. This causes some of the faults that I have worked out of my swing during practice to come back. When this happens, I go back to the basics and really slow down my practice swing. I also take a long slow breath in and out to relax while waiting for my turn. This brings me back into the groove usually. It is mental more than physical at our level.