I'm not sure how good your chances are since this was one of the discounted flights NW was offering over the Thanksgiving holiday whereby you received a confirmed BF seat for $599!! r/t I know lots of FT'ers & others signed up and will be on board--so I don't think its a case of either KL or NW having available seats (they were also offering coach fares of $211 r/t on these flights to AMS.
I actually booked a BF on that flight (with a return this Sat) and then had to cancel. I was told when I cancelled the flight was completly sold out in both classes.