Anyway, the reason I wanted a wide lens is because I still feel like I'm not capturing enough of the landscape.
Using an ultra-wide-angle lens to get everything inside the frame typically makes for boring images. They're usually more useful for emphasizing distance, or distorting perspective and foreground/background relationship. You may notice that the images you like most that were shot with an ultra-wide-angle lens have a strong foreground element; often the photographer gets really close to that foreground element, to make it more prominent in the image, while still including a vast landscape behind it.
To be honest, I find that I use my UWA lens mostly to photograph man-made objects. I'm not saying it isn't useful for landscape photography—I have used it for that, but I tend to prefer focal lengths in the 16mm–24mm (as it pertains to your camera), as well as ~70mm and longer. That's just me, though.
While the Nikon 14-24mm f/2.8 is one hell of a lens, it isn't the right lens for your camera. It is supposed to be a very wide lens for an FX camera, and doing that while also having a wide aperture and a well corrected lens is hard and expensive, and it makes for a heavyweight. With a DX camera, you can't use a lot of what it was made to be (because it isn't nearly as wide for you in practice), and this means the size, weight and price are basically wasted.
If you need the f/2.8 aperture, then the Tokina lenses are solid choices—either the 11-16mm, or the new(er) 11-20mm. If you don't, there are smaller and lighter lenses you can check out, like the Nikon 10-24mm f/3.5-4.5 and the Sigma 10-20mm f/4-5.6.