Hey Howdy Hey Jonathan and welcome to planDisney!
Welcome to the Passholder family Jonathan! You are in for so much excitement and Magic this whole year of your annual pass. Without further ado, let's talk about getting you into the EPCOT on New Year's Eve!
You are correct so far Johnathn, Annual Passholders do need a
theme park reservation to get into the parks. Looking at the
availability calendar as of this particular moment, EPCOT and Magic Kingdom do not have any reservations but Disney's Hollywood Studios and Disney's Animal Kingdom both have availability, which is subject to change. Since Annual Passholders have Park Hopping privileges, you can always make a reservation to one of the parks and then hop to EPCOT.
At this time, Disney no longer has any restrictions on theme park hopping hours. You may find it easiest to make a reservation for Animal Kingdom, which opens before Hollywood Studios, tap into the park and then head right over to EPCOT. Admittance into the parks is always subject to capacity limitations so the earlier you can get there the better. Keep an eye on your My Disney Experience app that day as Disney will typically keep Guests updated with park admittance there if they do get close to reaching capacity and stop letting people in. Park Hoppers are usually limited first so make sure you get there early!
From what I hear and see online, EPCOT and Magic Kingdom are the places to be to ring in the New Year and I hope you can get into the parks for the big celebration. Best of luck and please let us know if you have any other questions!
To Infinity and Beyond,
Nick