This sounds like a pretty epic trip, but I'm with Rocky, the distances are not to be trifled with. If you go from Rock Springs to Ashton via Salt Lake, that's not three hours extra, more like eight. SLC Provo Ogden are a full-house "metroplex" with multi multiple lane freeways and worse drivers than the East Bay or even Pugetopia.
Maybe you could choke off at Echo and turn for Ogden and THEN go north, but honestly, that's boring freeway. It's better to go north out of the Rock on 191, then crank a right, through Jackson, then over the next pass into Ashton.

There's another factor about Salt Lake. I don't know what the heck it is, but road signage in metro Utah is really confusing. You'd think on a temple grid square, it would be easy, but I swear I made more wrong turns, or got trapped in the wrong lane, more times in Ogden than I have in years. Don't count on your navigation system, either. My Dad and I had to turn off Bitching Betty 40 miles north of Ogden because SHE was lost. Honestly, I'd pass on Salt Lake, it's just a busy city.

And the Snowies in south central Wyoming should be nice. But that's not a simple route.
It's actually 130 out of Laramie west over a pass then into the Encampment Valley and a junction, north on 130 goes to Saratoga and then Walcott on the freeway, south on 230 goes to Encampment. West from Encampment goes 70, that goes up high and crooked and drops you into the Little Snake country at Baggs just north of the Colorado line. There you turn north on 789 up to the freeway at Wamsutter, west of Rawlins.

Taking the quickie to Walcott Junction on 130 only will save you miles and a couple of hours versus Wamsutter and backtracking to Rawlins to turn north for the Togwotee route to Ashton via Lander and Jeffrey City. Overall, I think that's better than Salt Lake. Both ways better than Salt Lake, the freeway north from there is pretty darn boring and kind of rough. Oh, I already said boring.


I like trains so from Laramie to Rawlins I go on 30 through Medicine Bow, that's a good highway with light traffic.

Up hills slow,
Down hills fast
Tonnage first and
Safety last.