Happily there is a fix. I use a major brand Arca-Swiss compatible L-plate on all my bodies (Kirk, RRS, I don't think it matters). So instead of screwing the strap lug into the tripod socket on the camera or the L-plate, I bought a Wimberly C-12 clamp (http://www.tripodhead.com/products/C12-compatibility.cfm) for each strap I use.
I do something similar, but I don't like the bulk of the Wimberley C-12 on the strap (I have C-12s on a tripod and a monopod, though). For the strap, I use a Kirk QRC-1 1" clamp, smaller and lighter, but just as strong. I attached the BR FastenR-3 to the clamp with a little LocTite Blue 242 (semi-permanent) on the threads, so no worries about it coming loose.