I think only MK has ever gone into phased closing so epcot I would expect to be packed with those drinking in the new year but not can't get in. Parking will probably fill up so it's a don't drive if you don't need to night.
for OP: marathon starts jan 2, many schools don't go back until jan5, some don't go back until jan 9. The trip is going to start very very crowded and end just crowded.
New years day, at least until mid afternoon tends to be very empty in the parks as everyone slept in. Great time to hit MK, especially at rope drop.
The NYE midnight fireworks are the largest display that disney does at MK. You can easily see it from resorts around it and it's a full 360 around MK including closing down boats and bringing out barges with more into the lakes. If you want to skip the parks (smart) but still see it, head to poly or GF. Maybe do a dinner at cali grill and watch from up there if that's on your meal lists (and there is room, they are probably booked tight).
EDIT:
Right now I'm planning on MK for dec 30th and might do epcot on the 31st. I more want to just say I did it once and film them from inside the parks.