I don't use MSP frequently, but... just happened to read this on the plane on the way to a one night stay at the MSP/MoA SHS in Bloomington. I asked at check-in and, much to my surprise, they DO have a stay with miles option on this. You pay for the room with points and pay either $10/day for outdoor parking or $15/day for indoor parking. The airport shuttle runs to MSP at the top and bottom of each hour. It took about five minutes to get from the airport to the hotel in a rental car.
The hotel itself is compact. The lobby and the rooms are smaller than most SHS. The bathroom is right when you walk in the room and the room itself is smaller than most SHS rooms, with the closet inches from the bed, but the room iteslf is clean. The tub sparkles. The staff had my feather free room ready and waiting, and I cannot hear any airport or highway noise in the room.
If you have any other questions, I'm here until eight tomorrow morning and am happy to ask or look.