I have had this occur a number of times. All I do is make as many reservations as possible to take advantage of the lowest possible rates.( theres no rule saying you must use the higher for the entire stay)
When I check in I explain exactly what I had done and every time the property has be able to combine the rates/stays on one folio.
There is no reason even to get a manager involved.

I suppose if the hotel in question is unwlling or unable to do that then just have them close each folio/reservation and settle appropriately.

mike