Once again, I'll say the same thing I always say about the issue:
KNOW the laws in YOUR state.
COMPLY with the laws in your state.
DOCUMENT the fact that you have complied with the laws in your state.
You will have no problems.
Yes, it really IS just that simple!
If complying with the laws in YOUR state means you can NEVER bring your RV into the state, then DO NOT bring it into the state, not even "for just a day"!
It is NOT illegal in any state to own a Montana (or any other state) LLC. It is NOT illegal in any state to have a vehicle registered to a Montana (or any other state) LLC that you own. It MAY be illegal to bring that vehicle into your home state without paying the applicable taxes.
Again, KNOW, COMPLY, and DOCUMENT!