I would definitely book reservations for this year, especially since so many people have taken up RVing.
I90 is the most direct route but it does take you through major cities. I've done it multiple times. Others may have suggestions to circumvent them but if you stay on 90 make sure you say in 90 express and not 90 local through Chicago. I've done that trip in three weeks (including Yellowstone but not Little Big Horn) so 6 weeks should be fine. Did straight shots out and back so not much advice on what to stop at. While you are in SD I'd go to Keystone. Very touristy and kitschy but fun. Bear Country USA is also very enjoyable. Treat yourself to elk medallions at Jackson Lake Lodge's restaurant in Grand Teton. Enjoy!