We've been the week after Christmas 2 times - I also work in education. I have the same debate about going next year- a shorter 4 day trip or the full week of Christmas.
When we go during Christmas week we find it necessary to be at each park well before opening since that's the least crowded time. I make my
DAS advance selections for the late morning and evening if possible. ADRs at sit down restaurants also help immensely. Counter service is very frustrating during that week, lines are ridiculously long. Pack snacks so you aren't stuck waiting in a 30+ minute line for Gaston's cinnamon roll and a bottle of water.
We can usually accomplish many rides in the morning with my DAS and low wait times if we are there before park opening. When crowds start to get crazy around 1 or so, we take a mid-day break at the resort. If we go back to the park afterwards we will only experience 2 or 3 attractions for the rest of the night. We will have a DAS lined up for one of the top attractions before we leave for our afternoon break. We will use that DAS when we return to the park after our break, grab another DAS with a wait time of 2 hours or so and go to dinner with an ADR. By the time dinner is done, our wait time for the DAS is pretty much over so we can experience that attraction. If we're lucky we can maybe get one more minor attraction.
We avoid going to the parks each day during Christmas. Schedule some downtime at Animal Kingdom Lodge to view the animals, make Disney transportation part of the fun, go to other resorts to have a meal and see the Christmas trees and Gingerbread displays, etc.
If you go in with different expectations you can definitely enjoy your time in the parks that week.