I have to say I foresee the end of the Wings Alliance soon, NWA seem to have a habit of locking KLM out of their systems according to the number of times I've rang UK Reservations to do stuff.
All I can say is ensure you get the NWA Locator at the same time as getting the KLM one, then just ring Minneapolis and get them to do it for you...
Unless you got the less than helpful b***h of a NWA supervisor who disagreed with the fare rules on the C class ticket I bought and patronised me and my good lady on the phone while we were in the US... UK Resv kept doing the change, NWA kept un-doing it.
I had to end up calling KLM Amsterdam from over there who read the rules and said "yes, date change can be done, I've done it and changed it with comments in there for NWA to leave it alone"