I'm right handed as well, and prefer to reel left, though if the rod is a already setup on the right I will reel it that way (esp. when on someone else's boat, or when fishing with people that reel right and might hand the rod off to them.) I just cast right then switch to reel.
I find it's easier to use my dominant hand to control the rod, hook set, casting etc. and never been a fan of switching hands back and forth for casting. I've noticed a lot of people from eastern canada that are right handed tend to reel left as well, and only noticed this many people that are right handed reeling right on the west coast.
My father in-law is a lefty and was the opposite, he would reel left after casting with his left hand, so when I started him off bait casting, I got him to cast with his left hand as that always felt the best and reel right. He found it felt more natural that the old switching method and is thinking of switching over his other rods the same way.
Personally I'd recommend casting with whatever hand is your dominant hand, and learning to reel with your opposite. You won't be wasting time switching hands and fumbling with the rod when you might have a potential bite. With the centerpin I use my right hand to cast and my pinkie and ring fingers as the drag (on an islander- not sure how that's not possible for others?) With the amount of control you need to cast a cp properly it would be like learning to write with my left hand.
Lots of great fishermen out there that do the switch, for some it's just "what they do".