I wouldn’t recommend that on the SD side. I know a group of OOS hunters that had tribal tags and were found on deeded and state land within the rez. They won’t have hunting rights for a year.When on the rez just hunt.
That said, that is a crap trade for ND. Until the entire rez is wall to wall tribal land, you’re not solving anything. The checkerboard of tribal, state, and deeded is what it is.