I got the idea from Neuro, but why don't you buy a clamp with a 1/4-20 threaded hole to attach to you Black Rapid strap. Then you just clamp your strap to the Arca Swiss compatible plate on you camera. When you want to attach the camera to the ball head clamp, then un-clamp your strap and clamp the camera to the ball head. No unscrewing the strap... which I agree is a pain.
For safety sake, I use a locking lever clamp with a lock button. It won't come off accidentally. The one I used that was 1/4-20 compatible (and it says it works with RRS plates) is a $55 Sunwayfoto DLC-42. It sounds like an unknown supplier, but their cost is low and I have been real happy with their quality. It has a nob to adjust it for your plate, and a lockable lever clamp (the nob won't turn and loosen when clamped if adjusted properly). Though you can use any Arca Swiss compatible clamp you want. Here is the one with the 1/4-20 threaded hole to match the screw on the strap:
http://www.bhphotovideo.com/c/produc...ver_Clamp.html





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