Have you considered hotels near Epcot on the Boardwalk? I also don't see any availability for Epcot on NYE. I do see stuff for the hotels, particularly Swan and Dolphin. It's not far.
EDIT: I think all ADRs opened up on time for NYE at Epcot, because I booked my ADRs for NYE on 10/27 and saw what appeared to be all of the restaurants listed. You might also consider hotels on the Skyliner.