And the DIY version of it : http://www.diyphotography.net/the-diy-r-strap

I tried such a DIY contraption (at home), and yes, it's quite easy and fast to reach to the camera. I stillhave to try it "on the field" with one or two cameras. The only part I found not satisfying is when you need to change lenses. The camera body doesn't stay in a position where you can easily mount/unmount your lens with one hand (the other hand being busy holding another lens).

...I'm forever moaning about it either cutting my neck to wear for easy shooting or making my camera inaccessable to me when it's under my arm...

For the times where you have to deal with only the standard strap, if you're right-handed, you can wear your camera *reversed* on your right shoulder, so that the grip faces towards the front, easily reachable by your right hand. It has another advantage : the lens, instead of pointing out on your side, lays securely against your body, pointing downwards.

[EDIT] I just realised that you being right-handed or not doesn't really matter, since you have to hold the grip with your right hand anyway