A 28mm on the D800/e would probably be fine.
However, over the years (back in the days of film and repelling into the depths of the canyon), I used much wider in places and a little longer in others. I used fixed lenses mostly back then, 18mm, 20mm, 24mm, and one 35-70mm. Anything much longer and you miss the grander, IMO. You could take two pix with the 28mm and stitch it in photoshop and with the 1.2x and 1.5x crops, still have some good quality details with the D800.
In looking at the metadata from my last trip there in 2006, the bulk were done with 12-24mm followed by the 17-55mm on my D2x. That would be either the 16-35mm or 17-35mm on my D800 today with few details shot with the 24-70mm.
The narrower-angle lenses work great for detail shots, but overhead looking up, I've found the wider work better for my vision.
A good option to consider would be to rent one of the wide-angle zooms for visit and then have a blast without as much effort to shoot the fixed.
Have a great time in the slots!