Not sure how you have a trip nailed down to the hour of extra time. Buffalo Bill Museum 100% would be added to the trip.
Also even if it added extra time I would cut more cross country rather than drive I-29 to Sioux Falls and then again 90 from Sioux Falls to the river. Stop to eat in small towns and see the country. I've also driven those routes enough along with I-94 across MN, ND and MT that I get off of them asap and parallel them on state hwys if time is not crucial.
It's a curse sometimes...
7/14 Friday - Drive to Sioux City Iowa and stay at XXX , 4:17/289 miles 5 - 10 pm
7/15 Saturday - Drive to Badlands NP 5:05/356 miles, then onto Rapid City 0:57/63 miles and stay at 8 - 1 badlands 2 hrs 3 - 4 rapid city, dinner, hotel stay at XXX Rapid City
7/16 Sunday - Visit Mt. Rushmore 0:31/23 miles and Crazy Horse Memorial 0:32/18 miles then onto Deadwood Blackhills National Forest, Four Corners 1:10/54 miles and stay at Deadwood
8 - 8:30 2 hour mt rushmore, 10:30 - 11 drive 11 - 12 crazy horse, Deadwood and Sturgis stay in Deadwood at XXX
7/17 Monday - Explore Deadwood, visit Devils Tower 1:16/74 miles and onto Sheridan, WY 2:28/163 miles 8 - 10 Devils town 10 - 11, 11 - 1:30 Sheridan Pinehaven Lake drive to Bridger over the Bighorn mountains 2:49/146 miles
7/18 Tuesday - Boat and visit Family
7/19 Wednesday - Leave afternoon sometime?
7/20 Thursday - Drive to Denver 8:20/550 miles Drive to KC 8:24/593 miles