I really don't see the logic in "gunning it across to San Fran" and then taking 10 weeks to drive back. Besides the fact it is a 6 day drive across the country, why race past so many great places. The idea of a loop is to take one route out and another back and pace yourselves accordingly. You mention mountains, deserts and rivers in your list of attractions and you will find no better place than on route through Colorado, Southern Utah and Arizona into California. We are talking some of the best natural wonders in the world, from Rocky mountain alpine scenery to the Red rocks of Arches and Canyonlands, Bryce canyon, Zion, Monument valley, Grand canyon to the hottest and lowest desert in the US in California, known as Death valley, where you can continue towards the coast via the Sierra Nevada, which is home to one of the greatest places on earth, Yosemite NP. You could easily spend a few weeks heading out west and then take the time to enjoy your southern route through Dallas, Nashville etc on the way back.
On the right of each page you will find the RTA fuel calculator and RTA reservations centre where you can get an idea of car rental and hotel costs. For example, a fuel estimate 8000 miles divide by 25mpg = 320 gallons x $4 per gallon = £1280. Rooms can be found cheap, but I would average around $80 a night for planning although they can be found cheaper. I usally consider eating in the US, no matter whether if it's take-away, cook, or eat out to be similar in price to the UK but with the advantage of the pound v dollar exchange rate. In other words a £30 meal here would cost $30 there, it's not exact but works for me. With car rentals you would have to check that your price is all inclusive of the young driver surcharge and remember, that will be for each person under 25 who wants to drive.
[Just noted your Yellowstone comment, but the same applies wherever you want to go. Take one route out and one route back and pace yourselves.]