my wife wants to see Memphis
OK, that helps. In rounded terms it is 1800 miles from the Alberta/Montana border to Memphis. As a minimum, I would make stops in the Black Hills and in the Northern Ozarks (around Branson). It would be about 600 miles to Rapid City and another 900 on to Branson. (Just using these specific cities as waypoints--not as the exact stops.) From the Branson area on to Memphis is another 300 miles.
From Memphis to the Tennessee area of the Smoky Mountains National Park is 450 miles. There are several choices of routes: one that would include Nashville, a southern route that would include Chattanooga, and of course, one in between.
I won't go into possible return routes, but in the Fall it wouldn't be bad to swing down to East Texas and back up through New Mexico and Colorado (or Utah).
Just some observations. We enjoyed a trip up from East Texas in July/August to Banff, Lake Louise, and Waterton Lakes, so we have some experience about that route.