The parks stay open quite late during Christmas Week. If you are already in Epcot you will have quite a bit of time from the end of Illuminations to make your way back to the International Gateway.
If you stay at the MK until a midnight closing or even late into the evening, you should take the bus back to the Swan rather than doing the monorail to the TTC and then to Epcot. For one thing, it will be faster. For another, you won't have to worry about not being able to get into Epcot.
On NYE, all the parks will stay open until either 1:00 a.m. or 2:00 a.m. (it fluctuates). The exception is AK, which tends to close around 6:00 or 7:00 all week.