Welcome to the RTA forum!

I think your route should be just fine if you've got a month to cover the ground. However, personally, I would add in Yellowstone on your leg between Mt. Rushmore and Utah. I'd also be curious if there is anything specific that you are looking at in terms of Native Americans in the Sioux City area. There certainly are some native american things in the area - as there are in most of the US - but there's no one thing there that stands out to me.

As far as the TripTik goes, the mileage should be accurate but the time estimates can be off a bit. Really, anytime you're trying to break a trip of this size down into hours, its kind of a pointless excersize.