I signed up for the Choice US program where I could transfer AmEx points at 1:1. But when I search for the Clarion CPH airport hotel for my date within the US Choice site, it says Sold Out for that night. However, if I search for a regular paid night either on the US Choice site or the Nordic Choice site, I can book a standard room for cash. I don't currently have any NCC points to allow me to try to book for a reward night under NCC.
I'll keep checking back from time-to-time and see if a reward night ever turns up.
Thanks for your help, GUWonder.