How to Fly by Mount Rushmore

I know we have a great bunch of experienced pilots out there so I'm hoping someone has had some experience flying by the Mount Rushmore and Crazy Horse monuments in South Dakota.

The chart tells me to stay at or above 7,700 MSL which puts me about 2,000 AGL. Seems awful high. I've seen some folks say to contact Ellsworth Approach and see if they can work me in closer. 

I am currently planning to fly into Custer County Airport (KCUT) which has a field elevation of 5,620 feet. My plan is to land there in the afternoon but take off at the crack of dawn. 

Any advice or information on seeing these monuments by airplane would be greatly appreciated!