Ernest, you'll be happy to know you took the EASY way across
I always assume if I take the rig that way I'll cut over at Casper then head up through Thermopolis. We were going to drive that way one year then ran short of time.
If you're going to kick around Sheridan in the toad, be sure and go to King Ropes downtown and walk out the back door across the alley to the museum. Kendrick house is interesting if you have the time. Drive past https://sheridaninn.com
and say "That is a lot of dormers."
The visitor center up on the interstate has RV parking and a nice view.
As you are approaching Sheridan from the south, when you're about even with Big Horn you can look left at the mountains and see a single forestry road heading up the side of the mountain. It's a short cut to Burgess Junction, if you don't mind 32 miles of forestry road. READ: NOT BIG RIG FRIENDLY. Campers and logging trucks run it, however. Our hideaway is up that road. I may or may not have driven a rental diesel box truck down that bad boy. I think the statute of limitations has run out.