I can relate to you except for the fact I haven't been riding street that long.Even if you have been riding a long time, do a school!
It is supposed to be pretty common for righties to prefer left turns since they feel that they are more in control when they can counter balance towards their "good side". I kind of remember being that way when I first started riding dirt on a tiny little kx50 two stroke, but I got over it by the time I was like 10(kx80 2stroke by then)from TONS of riding - I was a motocross junkie growing up, and although street riding is a whole different animal, the years of experience did help the transition feel more natural. I would blaze through the left turns powersliding that little thing, but always approched the rights cautiously - which is more dangerous because you lost concentration and just think too hard about the stupid turn and not your speed or lines.
Completing a riding course, even if it is just a basic one, will help your confidence a lot on the right handers - they are the same thing after all and its all in your head!
I took an MSF course two years ago, thinking it would just be a cakewalk for the insurance break, but actually left feeling more comfortable on two wheels just knowing that I completed the course - and I had already been riding for quite some time.
Same here. I get my knee like 6 inches off of the ground not counting slider distance.and one thing on riding dirt...most dirt riders dont like right handers because you dont have your foot next to the rear brake! LOL at least that was my thing...i loved squaring up left handers, but when it came to squaring up a right hander it was tough since i had to keep my foot on the peg and not out to put more weight up front.
as for leaning on a street bike...i cant say im uncomfortable with left or right handers, unless theyre slow, tight turns. but thats where clutch control comes in...just give it some revs and slip the clutch and if i accidentally give it more gas when turning right its no problem, because im slipping the clutch enough so there isnt much acceleration.
no knee dragging yet though...im gonna wait until i can hopefully take a track school for that kind of thing!