I'm surprised by the amount of confusion and misinformation in this thread. I thought people here understood the issues better.
You DON'T have to have a driver's license from a particular state or be domiciled in that state to register a vehicle there. All you need is a legal address at which it is "garaged." Just imagine you are a rich person who has homes in several states. You would have no problem registering vehicles using the addresses of those properties. The state you choose for your legal domicile is the one from which you will get a driver's license.
The key issue is not so much where you register the vehicle, but where you intend to keep it. To return to the OP's situation. If they had an address in SD and registered a vehicle there, but kept it at their property in MI it could lead to questions being asked as to why it carried SD rather than MI plates. All states have laws regarding how many days of a year a vehicle with out of state registration can be kept in-state without needing to be reregistered. Whether or not you get caught at it depends on how obvious your situation is. If you have to park your RV out in the open and you have nosey neighbors, it's possible someone will rat you at. If, OTOH, the RV is kept in a garage and is only taken out when you use it, the chances of getting caught are somewhat reduced. However, if you were in a traffic stop, a cop might, legitimately, ask why you have MI licenses and an SD-registered RV.
Forming an LLC in MT is a way to register an RV and avoid tax since MT doesn't have any registration tax. However, the above-noted considerations still apply. If the OP were to form a MT LLC but were to keep the vehicle in MI the same questions could be asked. MT LLC's work best for full-timers who essentially don't have a home state that they spend much time in. We are SD residents and have an MH with MT registration. We occasionally vacation in SD but the vehicle doesn't spend all that many days there so we don't violate SD law.