Upload & Sell: On
I think you need to evaluate which focal lengths line up with your vision better. 24mm is typically plenty wide for me other than when shooting indoors, but that is my style. If you are a really wide angle shooter then I agree with the recommendations to leave the 24-70 behind.
The trail seems somewhat long, not sure how much time you'll have to shoot. If possible, I would suggest a couple of different makeups, though it would cost $$$ since it's not what you have ready access to, but definitely save on weight.
Firstly, a micro 4/3 setup. You could have a huge focal length covered for less than the weight of just the 14-24, and have all the lenses readily available as you are hiking. Just a theoretical recommendation as I have no first hand experience with m43.
On the Nikon front, with a D600, I can think of many scenarios, but weight is always a concern, so here's my one suggestion from among many - D600, 24-85AFS, 70-300VR, 50f1.8. If your style involves a lot of really wides then the 14-24 in place of the 24-85. If you want to have a wider than 24 option just in case, maybe a used 20mm lens could be that "just in case" lens.
As for packs, the suggestions for a real hiking backpack, and working a gear storage solution into that is sound advice, but needs to be balanced against how often you'll want to stop and access or change photo gear. As for dedicated photo packs, I can personally recommend F-stop, though I have only used the Loka for long day hikes.