Way south through Wyoming? But doesn't I90 go straight across Minnesota? and on through SD and WY? Admittedly the only big town that far south in Minnesota is Rochester. I94 on the other hand goes 'way' north to Fargo, and south west along the Yellowstone to Billings.
When I last looked, Chicago to Billings was slightly shorter via I94. It's a bit closer to the Great Circle route. But the distance difference isn't much.
Then there's that US212 cutoff across the SE corner of Montana, which may shave an hour off the Buffalo Sheridan route.
Last time I drove cross country (in a car, not RV) I left I90 after Livington, took US212 over Beartooth Pass and Chief Joseph to Cody. Then US14 over the Big Horn Mtns and I90 across SD.
The return drive was from mid Wisconsin, so I took I94 to Montana, and angled up to Glacier at Billings.
Come to think of it, the first time I drove through Livingston, I was pulling a small boat nonstop Chicago to Seattle. I too US14 over the Big Horns, and gave myself half a day to see the sights of Yellowstone before going north to Livingston and the freeway.