Got it. OK just tried with a 70-200 2.8, wondering why I hadn't done that before. With a L black or smaller lens I have it on the bottom of RRS right angle body bracket. This places the orientation with the lens going perpendicular to your body. Imagine holding your right arm straight out to your right, that's what the lens does. It's a good position, well balanced and the knob keeps the back of the camera from hitting and rubbing your leg.
With the White L collared lens it now orients to the back. That is the front of the lens is pointing backwards. Well balanced, comfortable, works well even with the added weight. So you get lens pointed left, or lens pointed back.
The bigger issue is where is the camera grip? It needs to be in a good orientation (out) for easy grab. In both cases it is either pointing front (for the black L) or pointing right (for the white L). Both are the right spots for easy grab, the lenses and stable and secure at my side.
(Edit: using your nomenclature, with a black L the back of the camera is against your leg, with the white it faces forward. )
Phew ... when you said this I wondered if it would be a bust with L lenses but it works just great. Also, I tried the strap across the chest and it works as well as over the single shoulder.
Seriously liking this strap.