Now that I'm back from my 5-day backpacking trip, I'll add my two cents.
I decided to take the 24-105mm and the 70-300mm DO, and I'm glad I did. I think I remember one time when I wish I had the 17-40mm, but other than that I didn't have a need for it at all. I used the 24-105mm for about 70% of the shots. To answer one of the questions above, I took the 70-300 DO over the 70-300L because of weight and size. The DO version is more than good enough on my 5D3, and there's no way I'd want to add another pound and have to worry about damaging the L lens with the abuse that things take during a backpacking trip.
I have one caveat- my perspective on photos was very different than the casual GC visitor. Most people only see the canyon from the rim, so they want an ultra-wide like the 17-40 to capture it all in one shot. When you're below the rim, you don't need that perspective because it doesn't exist. When you hike down to the river and back, it's more like hiking in the mountains, where you want to combine wide angle and long-range shots. I'm definitely glad I chose to go with those two lenses.
Here's a quick shot (I haven't even started going through my pictures yet!) from night four, about 3000 feet above the Colorado River just off the New Hance Trail.