It would seem that I am stuck but was hoping that someone here has been in the same situation and found a solution.
I booked three rooms for one night using AMEX free night certificates. I then discovered that they were booked for the wrong night and went in to modify the reservations to the correct night. The system allowed me to make the modification (which it didn't used to allow, I should have know something would go wrong!), however, I then discovered that it had taken 240,000 points from my account instead of the free night certificates staying connected to the reservations.
I called in today to try to get this fixed. The rep tried to fix the situation by making a reservation for three rooms again (whereupon they would have cancelled the existing reservation, returning the points they had taken), however, the hotel is now fully occupied for that night, so no new reservations were possible. The first rep then put me on hold to try to find another solution, then cut me off (or, rather, transferred me to the timeshare sales people!). I called back and went through exactly the same process with another rep, they went to their supervisor and could give me no solution, although with the added wrinkle of trying to get a diamond force reservation with a certificate, which also does not work. I suggested that they leave the reservations alone and just credit me with the 240,000 points and cancel the certificates, but that was dismissed out of hand, without even checking into that possibility. That seems like a pretty straightforward solution to a problem that their system was at least partially responsible for.
So my question for everyone is, has anyone ever managed to get a situation like this rectified, and, if so, how?