Customer Support does not handle FCM’s - this falls under the Community team which also communicates if and when any FCM’s open up at the WoW Classic forums.
Since the thread has closed down 22 hours ago from now, its safe to say that FCM’s have stopped. Free Character Moves Starting Thursday at 1:00 a.m. CEST
Whether if they’ll be opened again, will depend upon server load amongst many other factors. But you’ll have to watch the WoW Classic forums for any possible update regards that I’m afraid.