From Keystone the fastest route to Moorcroft, WY is N to I-90 then west. 133 miles, 2 hr. 3 min. By US 16 it's 108 miles, 2 hr 4 min.
Not sure how you want to get to SLC from there, but if you go US 16, just past Newcastle, WY take WY 450 W to WY 59 N. Go on WY 59 3 miles, then turn left on WY 387 W to I-25. Go S on I-25 to Cheyenne and then W on I-80.
This goes through a lot of grassland and avoids mountains until I-80 near Laramie. Of course you bypass Yellowstone, Grand Tetons, and other spots, but it's the most direct way to SLC.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI