I'm in the same boat. I'm right-handed,but starting wearing courier bags on my motorcycles. Since you control the throttle and front brake with your right,I'd wear them on my right shoulder so if they shifted I could use my left hand. Never worried about adjusting the strap because I would always let the bag rest on the back seat. Now I just can't get into a left shoulder bag. (I also use the mouse left-handed,but that's another story)

I was looking at one of the customs on Reload's site,but after seeing the adjustment assembly on MDRawk's,decided against it because the buckle would be on top of my shoulder. I wound up buying a Bailey's Pro,and the strap is totally ambi(and very comfortable). The strap is reversible,and the buckle is in about the center of your chest. It's a size large,though,so it's too big for daily use and only hauls groceries and booze to parties. I'm using a medium Timbuk2,which rides fine on my shoulder,but is tricky to adjust. I ordered some 2" web strap and nexus buckles off eBay,and I'm going to mod the strap so it'll work like the one on my Bailey.