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For the most part, you will want stabilized lenses on the 7D for this type of outing. When you are hiking and continuously moving around, a tripod is not handy. In Zion, you will probably spend a lot of time on the trails or in the Narrows; so, you will be shooting hand held. A stabilized lens that goes wide to telephoto is ideal. I used my 17-55mm IS quite a bit. Since you do not own a stabilized lens below 24, I would take a monopod (a monopod/walking stick can be handy at times on some of the trails) and use the 10-22mm lens. The 24-105mm IS will handle everything else. At Bryce Canyon, the 10-22mm is deal for the most part, and I would try to use a tripod there. In Bryce Canyon you will probably not spend a lot of time on the trails since the view points are amazing. Again, you can get some wonderful shots with the 24-105mm IS also. A longer telephoto can also come in handy for some shots, but just a few. In that case, I would take one of your 70-200mm IS lenses. At the Grand Canyon in Arizona, a wide angle lens is ideal; the wider the better. However, if you go into Colorado to Mesa Verde National Park, then a longer telephoto lens is good to have; like your 100-400mm IS. For the most part, I seldom use any of my primes when I visit these places and the wide angle zooms typically get the most use. It is very difficult to zoom with your feet. So, I prefer the zooms under these conditions. And, today's zooms are excellent.
The bottom line is to enjoy the views and capture as much of it as you can; without spoiling the experience.