Since the OP specified they want to take their time and avoid cities it sounds like they want to see things rather than travel on interstates. This is how we always traveled. Does it really matter if you go slower and perhaps go out of your way a little?
I would recommend that this trip begin at least by the end of August because you'll have some mountain areas & you want to be out of them by the 3rd week of Sept. Have your Senior Pass for entry into national park/monument areas or purchase the America the Beautiful Pass which will give you a year's entry. You'll see some beautiful color getting into September.
So.... here's a rough route and you can add or subtract. Perhaps you've never seen some of these sites:
From Dallas take OR 97 south to 26 east. Stop at John Day and explore. The state park is very nice. At Boise, ID take 55 north a short distance to 21 to Stanley, ID and view the beautiful Sawtooth Mountain Nat'l Rec Area. Then take 75 south through Sun Valley, ID to 93 east and tour Craters of the Moon Nat'l Monument in Idaho.
Then take 26 to I-15 to ID 30 to WY I-80 to 191 south at Green River, WY. Drive 191 through Flaming Gorge Nat'l Rec Area south to Vernal at Dinosaur Nat'l Monument. Take Hwy 40 east to 64 east to Rangley, CO. At Rangley take 139 south to I-70 to Grand Junction, CO at Colorado Nat'l Monument. There's a nice state park at the park road entrance on the Colorado River with hookups.
Then continue south taking CO 50/550 to Ridgeway, CO and pick up 62 to 145 at Telluride. Take the free chair lift for a great view of the area.
Continue south on 145 to Cortez, CO and tour Mesa Verde Nat'l Park. Take 160 east to Pagosa Springs. Spend a night or two and take in a awesome soak in the immaculate small pools of varying temperatures overlooking town and the river. We easily spend 2-3 hours here. Pack a small cooler.
From Pagosa Spring head south on 84 to Chama and Abiquiqu, NM. In this area are Taos, Santa Fe (it will be chili roasting time along the street corners - great smells and food). Bandelier Nat'l Mon. is also great to tour along with Los Alamos.
From Santa Fe take 285 south to Carlsbad Caverns Nat'l Park. We've stayed at Brantley Lake State Park to tour.
Then continue working you way into Texas via the Hill Country and on to Louisiana.