I tend to leave one around my neck or shoulder and the other in my bag. I just got a Lowepro Inverse 200 hip pack that'll be especially good for this.
I've got an Optech strap that has the connectors that can detach from the neoprene part of the strap; I connect the remaining "connectors" (the parts that are actually attached to the camera itself), creating a decent hand strap. You can buy extra connectors for the second body, so either one can be worn around the neck or shoulder while the other is in the bag and can be grabbed by the hand strap when it's time to shoot with it.
On the subject of Optech, they do have a strap that holds two bodies:
Reporter Strap | Demo Page
I've never tried it myself, but that's an option if you don't mind carrying all that weight on one strap.
BTW, on the issue of left-hand vs. right-hand, I'm actually ambidexterous...I do some things left-handed and others right-handed. With my photography, I really don't find a need to have my shutter button on the left side, but I'm left-eyed when it comes to the viewfinder.
HTH,
Heather