I use Canon E1 handstraps on both of my bodies, and they're great, but they require a battery grip to attach. The new Canon E2 strap comes with a lug for the tripod socket, but that would mean detaching the BR lug. If you use the Arca-Swiss system, some camera plates/L-brackets have the slot for a handstrap, and a 1/4"-20 hole for the BR lug (although I have my FasterR-3 attached to a Kirk 1" clamp that I then attach to a camera or lens plate as needed.
Thanks everyone for your replies.
Neuro, your setup is identical to mine, RRS L-bracket, BR strap. I just bought a Canon E1 strap off of eBay for $5 - it looked legit but time will tell. I have seen the Kirk plate and BR combo before - it looks pretty slick. You must keep your L-bracket and hand strap permanently mounted, correct?
I like the L-Bracket on the camera as it adds a nice later of protect on two of the planes. My 40D L-Bracket has the loop for a hand strap but I can't tell of the 5D3 has the same provision, I can't tell from the photos. I will call RRS on Monday to inquire about this and I will place a pre-order over the phone as they owe me free shipping on my next purchase.