Hello and welcome to the RTA forums !

I'm not sure about the Las Vegas/Los Angeles part, we've been there a lot so it's not a big deal if we don't go, but I don't see anything interesting to do between Salt Lake City and San Francisco.
I really can't see the point in driving all the way to LA to sleep a night there. Personally from SLC I would head across the Great basin via West Wendover, Ely, Tonopah to Lee Vining and then spend some time in Yosemite NP before continuing to SF. You could also head to Reno and Lake Tahoe and maybe even across to Napa valley, but Yosemite would be my first choice entering the park via the Tioga Pass (CA120) which is a fantastic mountain drive.

- 3 days at Yellowstone, last night at Pocatello
Did you consider Jackson to give you some time in the Grand Tetons ?

I think you have a great trip to look forward to !