Avoid MK like the plague for the weekend after Thanksgiving; locals with their families add to the resort people already staying there.
DHS is also crowded because of the Osborne Family of Lights that weekend as well.
Most families leave late on Saturday night from Thanksgiving week, but some still leave on Sunday.
Monday through Friday it will be good, but the following Saturday it will start picking up again, between the parade taping over the weekend - and the Pop Warner people arriving.
I strongly suggest that you have dinner ressies at least through Sunday night of the first weekend. I took a few friends a few years ago, and they insisted we go with no plans. After walking around DHS for an hour on Sunday night with no place to eat, we finally ended up back at POR. They were also booked. We finally took the boat to DTD to the Rainforest Cafe. By then it was almost 7:00 pm - we ended up sitting outside, but it was pretty chilly, otherwise it would have been a 2 hour wait. We got about halfway through our meal, asked to box the rest of it up and we went back to our room.