On the other hand, if the 70-200 is in my backpack, what good is it going to do me?There are two approaches for this
1. Leave the 70-200 on the camera, and only change it when you need the wider perspective of the 15-85. Your landscape shots aren't gonna disappear in a second like a critter at 200mm will. It was my strategy for Glacier (always leave the 100-400 on, have the 11-16 on my belt) and allowed me to get bear shots, etc.
2. Not sure of the hike and how much scrambling, but if you can clip it onto you at the belt or your pack allows you to have both lenses accessible at any point. I had a Capture clip on my pack, so that my camera was always accessible, and then I had a carrier on my backpack belt for the other lens. But, that was for more traditional hiking and it wouldn't work if you are scrambling up canyons