I've driven from Utah to Minnesota as part of a larger road trip. I too have a Utah permit.
To stay in states that honor my permits, I went up to Hwy 80, then as mentioned, crossed South Dakota on 90. From there you can take 29 to 94 to get to Minnesota. Your Utah permit is good in Minnesota.
But, I should mention Hwy 80 was under construction. Probably still is. I left Hwy 80 in Rawlins, WY taking 287 to Casper, then Hwy 25 to 90 east. Beautiful drive in mid-Wyoming near the Devil's Gate, towns like Muddy Gap. LOL.
If it's a casual road trip, you can venture into the Black Hills in eastern SD. I gambled $2.00 and won enough to pay for parking and a tee shirt in Deadwood.
If you want to go through Nebraska, you can open carry. But, as stated, you have to unload and store in Iowa. I spend time near Sioux City, but use hotels in South Dakota. I've limited open carry in Nebraska to my car, so I can't say anything about how people react.
Hope you enjoy the trip.