We did a trip of similar craziness in a tiny TT from the southwestern corner of California, across the south, up the east coast into Canada, and back home diagonally across the US in the early 1970's. With two small children. Ten weeks. It took two years to plan (without internet). Was it worth it? YES! The memories of a lifetime were made. Of course, gas was about 25 cents a gallon then and our old 6-cylinder Ford was a frugal user thereof.
Put a US map on your wall so you can visualize this project. Stick pins in it for the places you want to visit. If you have to do the entire loop and be back home by a certain date, the itinerary will have to be followed carefully or you won't make it. Be sure to be flexible enough that you can accommodate illness, bad weather, and mechanical troubles. If you have endless time, it will be different.
Think of plan B for each of the big national parks because staying in them might not be possible. At least with a TT you can camp outside the park and do the day use thing.
Have a great trip!