The week between Christmas and NY is Holiday season - so, it will be the most expensive time. The only way to get around this is to check in Christmas Day. That's what we did last year, Christmas Day to New Years Day, and we got the "value season AP rate" for the whole stay.
New Years Eve is so cool. Our experience may have been a bit odd...We went to AK around 12 noon - 5 pm (not really that crowded), Yachtsman Steakhouse for an early dinner (5:30) - this was wonderful! Yes, it was more expensive than a regular dinner there, but it was still great! Then, we went over to World Showcase. We walked right in, hung out in UK and watched that "beatles band" (I'm stumped for the name). Yes, it was crowded, but and extremely happy crowded. Everyone was polite and friendly. If we didn't have children back at the kids club and if we didn't have to leave so early the next morning, I would have stayed there until midnight. We did see the MK fireworks, though, from our balcony at the GF! OMG!!! What an incredible experience. I have NEVER seen a fireworks display like that. Definitely worth it for me!
Hope things work out for you!