I think you may need to mix up your drive times a bit with some longer and some shorter days. In '13 we did a spring/summer cross country loop in 30 days and 7000 miles.
We did a bee-line across from VA to the ancient puebloan ruins in Mesa Verde ,CO (mostly on I-40), 4-Corners, then a Cirque du Soleil show in Vegas, new transmission in San Diego, visiting family in Santa Barbara, Grand Canyon, Yosemite, Yellowstone, Mt. Rushmore, Black hills, and lots of little attractions in between. I know the order is off, but that is sort of the highlights. The return was mostly I-90 and I-64 as I recall.
We never stayed anywhere more than three days, which is 1 day too many for me, and we never felt hurried. We only had reservations in Grand Canyon, Yosemite, and Yellowstone NPs, everything else was just researched and booked as we went along.
Enjoy your trip!
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