@Brian_W_Downs This sounds really exciting. Congratulations! I have not done this, but I have done the South Rim to river and back twice. I think there are a lot of variables, and someone more experienced at hiking or photography will probably have better input, but I’ll put out some questions and comments for you.
First, how do you like to shoot landscapes?
Do you prefer a lot of telephoto or wide?
Do you hope to do some astrophotography? The night skies are amazing there.
Are you good at spotting wildlife?
The first time I went was in the film days. I don’t remember what I had, actually. The last time I went with a Sony a6000 (APS-C) and an 18-105. I am not a strong hiker (very poor, in fact), but I think even for many people weight is a serious consideration since you’ll need to carry a lot of (heavy) liquid, food, etc. Depending on your goals and photography style, I think one lens is a great idea as long as you won’t have regrets. I feel like I was satisfied with my one lens, but I wouldn’t want you to have regrets on my account. 
If you are good at spotting wildlife (I don’t excel there either), you might want more telephoto than 105 (crop or full frame?), but other than that I personally would find the mid-range zoom or possibly the wide more useful overall, especially if you are okay with cropping if needed to make up for lens limitations.
If you haven’t already, you might want to search some of the photography sites that have EXIF info (i.e. Flickr, 500px, or ?). Find the types of images you like and check out the focal lengths people were using. Just a thought. I’m really interested in what others have to say as well!
**Quick note to add - I just did a brief look at the favorites I posted on my 500 px account and they are almost all wide. I had mostly 18mm (24mm FF equivalent) and one at about 100mm (150 equivalent). However, my taste seems to run more to wide, so…take that for what it’s worth I guess. 
