I think you will find if you go back to posts from this past Dec that you are going to be there pretty much the busiest week of the year. There were several days this past Christmas break where the parks closed because they were full. If you go the next week, the parks will be almost empty (which of course only works if you don't have kids in school).
I've been told that from 12/24-1/1 is very busy, but the week after Christmas is slower. I was just trying to figure out when most students go back. My sister was there from 1/1-1/8 this year and the crowds were low.
My DH's break is just from 24th to 1/1. That means we fly in on Saturday and back on Sunday. We will try to hit the parks early, FP attractions, leave in the afternoon, and avoid MK on Christmas Day and NYE.
My children go back on January 3rd. They go to a Catholic School so I'm not sure about the public schools in NC. However, the dates are usually about the same.
In North Fulton County, GA (Atlanta area), the kids don't go back until 1/9. I am thinking the week after New Years is going to be much busier this year.