For the sake of Coke vs. Pepsi there is also the Carryspeed FS-Pro; I have one and like it, but I haven't tried the BR parts for comparison.
I regularly carry my 5d3 and 70200 2.8 ii on a black rapid strap (both the double and the spot version) with absolutely no problems or worrys.
I usually keep it attached to the tripod mount just so that it is more evenly balanced
ditto, I carry the 100-400L with the 5D3 (similar in size to your combo) with the RS-7 and jave absolutely no issues or worries. I leave it on the tripod mount at all times. Its just so much more comfortable with a 5+ lb setup on your shoulder as opposed to your neck like the canon strap.
I usually carry this lens, attached to a gripped body, with the lens facing backwards between my left arm and torso. The camera body then rests against my arm and torso. I've seen a pro do this, and copied the technique. It's surprisingly comfortable once you get used to it. I usually keep hold of the neck strap with my right hand just in case.
Share your experience please...I've always attached the strap to the camera body and carried the 70-200 that way -- with numerous camera bodies over the years. Never had a problem with the 70-200 affecting the mount.