Love the Teddy.
I believe it was still the TR National Grassland when I first visited the area south of Medora while on a dinosaur fossil excavation project in 1975. Wikipedia, at least, confirms elevation to NP status in 1978.
I did some traveling through the area in my '79 IH Scout while on vacation with the wife in 1982. We camped along the Little Missouri River near Pretty Butte, reportedly the site of TR's first ever bison kill (sidenote: while TR is rightly praised and memorialized for his immeasurable contributions to the conservation of Federal lands, his biography details a staggering history of slain wildlife for specimen collecting). The point here is that there is a unit of Federal grasslands south of the Southern Unit, more or less between I-94 and US 12 which parallels it around 50 miles to the south. While there are surely some sections and partial sections of private ranchland, at first blush it would appear that a fairly broad area is subject to exploration and disbursed camping.
I last stopped through our dinosaur dig site in 2002 and some indication of our field facilities are still visible. The bentonite clay soils are very fragile, so where disturbed by construction of our latrine (featuring men's and ladies's rooms for our group of 30 geologists and paleontologists), the scar and slight depression was still visible 27 years later. Of special note to potential Wanderers: You don't want to be off pavement or graded gravel surface in the western ND badlands when it's wet. Those bentonite soils are of the high shrink/swell variety, and when wet they form a gumbo clay which has no bottom.
It's very nice territory, and you've sure enough got it to yourself!
Foy