I am right-handed and left-eye dominant. I shot RH with the left-eye closed for 28 years. I switched to LH shooting in 1995. I had plenty of success shooting RH but I've never regretted making the change.
I've trained a lot of people (4,000+ teachers in NASP). It is common for about 10% of people to shoot LH but twice that number should. I've seen folks that had shot for decades with the RH switch to LH because of the dominant eye issue. Many of these folks will shoot the tightest groups of their lives in just 2 days. They are VERY excited about this.
Bringing the string to the dominant eye side of the face results in better depth perception, better peripherial vision, and for some folks better balance. For me it also provides a more relaxed feeling when I shoot. Try it, when you close an eye you can feel a bit of tension in your facial muscles.
A HUGE side benefit to switching. If you get some good instruction (coaching face to face or a good DVD) you get to start over and dump every flaw you've been taught or picked up in your archery life. That was the biggest positive for me. I had TP so bad in 1995 (had been coming on since 1981 or 1982)I was about done with archery. Starting over LH saved archery for me.
And no, TP didn't come back because I learned what causes it and how to prevent it.