NEW ROUTE I TRIED LAST YEAR
Believe it or not the best route I've found, at least from Duluth,MN, is to take I-94 to Billings, then south to Lovell,Greybull, Basin and into Worland. You pickup US 20 in Worland, all the way to Shoshoni. Take US 26 west to Dubois, Jackson and on to Alpine. And, yea take the Pavillion shortcut south of Shoshoni, WY Hwy 134, which by-passes Riverton. I always fill up in Shoshoni. This route is 100 miles longer but cut my driving time by 3hrs. Used to take MN 23 to I-90 to Buffalo WY and over the Bighorns to Worland. I also tried the WY 59 route (I-25 out of Casper, to 387, to 59 into Gillette, once), and the Casper to Lusk to Edgemont, SD, to Hot Springs, SD, to Rapid City, SD where I caught I-90. Tried that way twice, once on the way home and once on the way out.
After 13 yrs. of going to Jackson for the Hillclimb and riding Union Pass and Togwotee I'll take the Billings route from now on. Too much wind and sketchy conditions all around Casper WY. Glad I had an inline trailer when I passed a semi once last year, she may have gone over with a 8' wide deck-over.
Just my .02. Good Luck