This was hard.
First, the Canyon is big. Really big. Grand... I was at an exhibit at Grand Canyon Village and a tourist wondered where Skywalk was. When I told him it was 200 miles and a 5 hour drive to the west, he didn't believe me. It took reinforcement by a Ranger before he began to have a sense of scale, and we were near the center of the Canyon, not at its easterly limit.
Its scale means that when you look at it, you cannot see all that is before you. Your eye picks out a succession of formations, taking in the view a piece at a time.
The camera does not do that. It will either grab a wide angle image of multiple formations, a series of cliffs and chasms, or it will select a small component. Shadows are black if you expose for a sunlit wall, and my strobe is just not strong enough to light a ravine a few miles away. The sunlit areas bleach out if you expose for shadows.
My shooting was an evolution. First, I tried for big views, using an exposure tending toward the lit areas and using post-production to bring up the shadows.
Next I tried to capture prominent features and colors set against the far expanses.
I tried using natural features to frame the canyon.
I tried selecting prominent natural or unique features.
Whatever you shoot, you are shooting down - way down - unless you are able to descend into the Canyon.
Finally, I accepted that the Grand Canyon is too grand for me to capture with my little camera and lens. I picked a few points that allowed me to show them confined in a way that I could grasp the image with my eye.