Ambitious? Big understatement!
If your goal is a whistle-stop tour with virtually no time to explore and probably not much energy either due to the long hours behind the wheel, then go for it. I like a good speed run...for 2-3 days! But for 27 days? No way.
We generally recommend that people limit their daily travel to no more than 500 miles. Even this can be wearing on a longer trip and only leaves minimal time to sightsee/explore along the way. Thousands of miles of road-tripping has convinced us that you need to figure that you'll average about 53mph east of the Mississippi and 57mph west of it. This average factors in time for traffic congestion, stopping for fuel, and very quick stops for something to eat. No lingering.
Since you're camping a lot, I'd advise you to get on the road early. It's a good thing that you're traveling during our longest days because there's nothing worse than getting to a campground after dark to put up your tent, imho. However, even though it's light, most parks do have "quiet hours" starting at either 9 or 10pm. So you'll want to get there to have your tent up before the quiet hours start so you don't disturb others. On some of your legs, this is gonna mean getting up and going at the crack of dawn.
I took the time to plug your route into MS Streets & Trips. Here's a breakdown with comments:
* Blackwood, 543 miles, do-able. This is fine.
* Baltimore, 146 miles, leaves lots of time to visit friends and family. Good.
* Nashville, 703 miles, 13 hours on the road. Yikes! Good thing you're staying 2 nights. You won't have time to enjoy all the sights along the way but at least you'll have a day to enjoy Nashville.
* New Orleans, 531 miles, this is fine
* Dallas, 521 miles, this is fine, too.
* Denver, 881 miles, 15 hours on the road, another Yikes! Too bad you won't have time to explore along the way. If nothing else, you might want to squeeze in the memorial in Oklahoma City but even that will be tough in the time you have.
* Grand Canyon, 680 miles, 12 hours on the road. This is a double-Yikes! due to the fascinating sights you'll be missing here. No, you won't have time for Pike's Peak. And you won't have time for all the other fascinating things on the way there like Mesa Verde, Durango, Leadville, Aspen, Vale, Million Dollar Highway, etc. Your quickest route is to take I-70 west to 191/163 to Grand Canyon. Too bad you won't have time to enjoy Vail, Glenwood Springs, Moab/Arches National Park, and more along the way. This is a fascinating section of the country.
* San Diego, 559 miles, 10 hours. You'll have real limited time to enjoy some of the Route 66 types of sights like Kingman, Seligman, burros in Oatman, Barstow, and other points along the way. It's a do-able day but it really limits your time to explore these places.
* San Francisco, 512 miles. This is if you go up I-5. There's no way you can do the far more beautiful coastal highway in the time you have. Too bad. Taking the coastal highway is about 600 miles so the mileage isn't that much farther but the time to drive it is much faster due to many narrow, curvy roads and traffic. But it's so worth it. You would need 2 days to do the coastal route. Along the way, you could have enjoyed Big Sur, Santa Barbara, Hearst Castle, Monterey, and more. Too bad you won't have time. So I'll have to say Yikes to this one, too, just based on what all you'll be missing along the coastal route.
* Seattle, 808 miles, 14 hours on the road. Another big Yikes! This is if you go up I-5. You really should take at least 2 days for this drive. You're going to miss out on enjoying places like Ashland, OR (a charming town), Crater Lake, The Oregon Vortex, Wildlife Safari, the many beautiful things to do/see in Portland, Mt. St. Helens (the biggest must-see in Washington, imho), and more. Of course, you're totally skipping the coastal highway which would need a good 3 days to take between SFO and Seattle. 3 days minimum, that is. The northern CA and Oregon coast drive is one of the most beautiful drives there is, imho. Again, it's a shame you'll miss it.
* Yellowstone, 803 miles, 14 hours on the road. Another Yikes. And, again, the stuff you'll miss along the way. I don't bother listing them at this point but I just really don't see how you're going to have time to enjoy Yellowstone. You'll be able to drive through it but you really won't have time to see much. The crowds will be thick and just driving to see the highlights there will be slow-driving. It's a shame to zip through this so quickly.
* Mt. Rushmore, 505 miles, a reasonable day. But if part of this is spent driving through Yellowstone, it's going to increase the travel time a lot. You might have time to squeeze in a drive-by past Devil's Tower on the way but you won't have time for all the other wonderful stuff near there like Deadwood, Badlands, Black Hills, Wounded Knee, Crazy Horse Memorial, Wind Cave, Wall Drug, and more. I have to say Yikes! to this one, too, just based on what all you'll be missing here.
* Minneapolis, 634 miles, a bit long but do-able. Why 2 days here? I would take at least one of those nights and add it to either Yellowstone or Mt. Rushmore.
I'm not going to bother with detailing the rest of your trip. You start getting into more do-able mileage/distances at this point. Too bad you're rushing through most of the rest of the country.
My advise is simply don't do it! I think you'd have a wonderful trip if you just went as far west as Colorado or so, no farther, and back for this trip. Then another time fly to the west coast and rent a car to tour the western portion.
