I use right because the shops in my neck of the woods stock right wing feathers. If they stocked left wing, I'd buy a left clamp and use left. I use what the shops stock in case I need feathers in a hurry and don't have time to order feathers and wait for them to come in. Besides that, I believe in supporting the local shops. As far as accuracy and how quick they straighten, I've never seen a hair's worth of difference between left and right.

Really, I think what you've noticed with your arrow flight is just how much quicker feathers stabilize an arrow than vanes do. Also, since feathers are a lot lighter than vanes, you definitely took weight off the tail end of your arrows and moved the center of balance forward. That's the front of center balance, or FOC that you see discussed from time to time. Moving the center of balance forward will also help an arrow stabilize faster.