We did Christmas and New Years a few years ago and are doing it again this year with our family of 6 (2 ad, 17, 15, 7, & 5). I did all the research I could for Christmas time when we went and I knew to expect huge crowds, long waits, little ride experiences, etc. I had all my ADRs booked according to the parks that have late EMHs, we love the late hours and this is how we always do WDW.
So we got to Magic Kingdom early Christmas morning, the place was not busy looking at all, we went straight to get my daughters hair done at the barber shop and then to the Castle for breakfast. The park still wasnt crazy busy after breakfast, but it was the craziest later in the evening. I called it "butthole to butthole traffic.

You moved an inch every few minutes when going down Main Street. We didnt let that scare us off, we stuck around and by the time late EMH hit, it wasnt that bad.
So, this year we are trying the same thing, we will be at MK all day, we will not leave for a break, we will eat breakfast in Cinderellas Castle! I expect crazyiness, way too many people and a lack of personal space there.
Are you staying on property? You keep saying your cabin, wondering if you mean the Wilderness Cabins or elsewhere? If you are on property and you said how expensive it is to feed teenagers...have you looked into the free
DDP while there? We did it that way last time and also have it this time. It is saving us a lot of money. Just a thought!
Best of luck to you!