It's possible to get something for the week after Thanksgiving at a non-home resort, but you'll need to call as soon as MS opens on the first day your 7 month window opens. You should be prepared to waitlist if what you want isn't available. You will have lots of competition to get into one of the smaller resorts (VWL, BCV & BWV) for that time of the year.
To get into the BWV that week, your best chance is a Pool/Garden villa. That booking category makes up about 60% of the available rooms for the resort. The Boardwalk view and the standard view rooms make up about 20% each. BWV owners will book up the BW view and Std view rooms for that week on the first or second day the 11 month window opens. Those two views are very, very popular, and October - the first few days of January is the most popular time of the year for the EPCOT resorts.
Lake View will be your best shot for BLT. The standard views and Magic Kingdom views book up early in the home resort period.
At AKV, savanna view will be your best shot, followed by the standard views. Concierge will be virtually impossible and the value category will almost as unlikely.
DVC members do love a bargain (as well as an opportunity to be pampered, LOL).
OKW will be a possibility, but again, you'll need to book as soon as you can. Points are lower at OKW than at the other resorts and so space will fill quickly.
The above comments apply mostly to the time you want to travel - Thanksgiving to New Year's. Early June is s LOT easier to book at 7 months. If you call when your window opens, you should not have trouble finding what you want. That said, the "bargain" booking categories and concierge and the BW & MK views will always be very hard to get at 7 months, no matter what time of year you travel.