I've been many times to WDW over Thanksgiving. We always spend Thanksgiving at MK and it's crowded, but not unbareable.
We usually spend Friday at AK, Saturday at MGM and Sunday at MK for the early entry. We have never had a problem and it gets lighter as it get toward the following week. That being said, you may do better doing non Early Entry parks those days. I don't have any experience with them.
Looking forward to Thanksgiving again this year and I expect it to be busy Thanksgiving week and a lot less crowded the week after.