As above. If you want to stick close to your '8 x 6 hours plan' then all you can do is see where each route would take you and best suit your interests, there is no generic 'best' option. To get close to 6 hours on the road you would be looking at options every 350 to 370 miles but to suit your interests you could do less miles one day and a few more on another. Just to fit in SLC or Nashville and Austin would have you going over your said goals, but perhaps by only 30 mins a day. Interstate 70 is one of the most scenic of all Highways and would give you a taste of the Rocky mountains alpine scenery. You could check out some of the 'wild west' and head from Moab in Utah [Arches National park] down through Monument valley and perhaps spend a little time at the Grand canyon. That to would add a little overall time to your journey but in my opinion worth every moment.

Whie travelling west it would make sense to try and find lodgings on the west side of town so that when you are heading off in the mrning you are heading away from the work traffic. I wouldn't always plan to only drive mornings, you might find a place of interest 2 or 3 hours into your journey, where you could spend a couple of hours, have some lunch and continue in the afternoon, it would certainly give you more freedom.