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+10 to a properly fitted non-photo pack. For this, I'd take my 55L Gregory with a Mountainsmith Kit Cube in the top.
I also agree that this is WAY too much photo gear for a backpacking trip. Heck, it's too much for an ambitious day hike. This is why I got the NEX-7, though the D600 is definitely an improvement on earlier heavier FX Nikons.
Here's what I'd take if I wanted to have an SLR:
16-35VR (in your case, the 14-24, but keep in mind that it's a tank)
35/2 or 50/1.8G
85/1.8G or 105/2.5 AIS
70-300VR/VC Nikon or Tamron
That's still a lot, and there will still be some hard choices. Particularly if I were to take the 50/1.8G, I'd probably drop the short tele prime. There's absolutely no way, though, that I would carry the 70-200/2.8 or the 24-70/2.8. Way too much weight and bulk.
Sounds like a great trip -- have fun!