In the past 12 months, we tried, arguably, both the busiest and least busy weeks of the year. The week after Christmas had some real advantages, IMO. The weather is cooler, so we found it easy to go all day without returning to the hotel (we can't do that in the summer). You can get just as much done as you would on a day with shorter lines, but it will take all day to do it. However, with the weather not dragging you down, you can really take advantage of the extended hours.
The benefit to waiting in line is that you can really enjoy those well-designed and entertaining queues that would would breeze right past at other times of the year.
You could also bring some easy games to play in line - pre-made hangman game boards, Disney trivia cards, etc.
Make ADRs where you can. Seating at some of the CS restaurants is a nightmare; those were the only times we didn't enjoy last Christmas.
I have no advice for NYE. *laughs* I found the crowds in Epcot last year to be just too much for me. Just getting into Akershus where we had reservations and back out of the park after eating was stressful. Crowds really don't bother me that much generally, but I found those particular crowds to be over my limit (though it was day 10 or 11 of the trip, so I might have just been at my personal limit).