The value periods are (Jul 20 - Oct 1 and Nov 30 - Dec 18) and from about 1 Jan 09 to mid-Feb (except Martin Luther King weekend)
As far as smallest crowds between now and Thanksgiving, from 29 Aug to 21 Sep is the lowest period. 24-26 Oct and 31 Oct-2 Nov are also good weekends with low crowds, but the hotel cost will be higher then.
But take into consideration that during low crowd times, you also have shorter park hours, simpler parades, less street entertainment, etc.
Also, 29 Aug to 21 Sep is in the value season, so you'd be better off then from that standpoint, but it is still hot in the beginning of that period and cools off toward the end.
You also will be competing with Pirates and Princesses, MNSSHP, and Night of Joy, and I'm not sure if the dates have been firmly established for those things yet.
But why do you have to do this before Thanksgiving? 12-14 Dec has low crowd levels, and is in the value period.
Once again, I'd also consider park hours. You may want to go sometime during the value periods when the park hours are a bit longer even though the crowds are not at a minimum.
If you're interested in longer park hours, I'd suggest considering 15-17 Aug or 22-24 Aug. It will still be somewhat hot (not as hot as July) and moderate crowds but not too bad. And you are likely to have good late park hours. Still may be competing with P&P, but there's no way to tell until later in the year. 26-28 Sep same thing, only cooler weather. Getting into tropical storm season, though. 4-7 Dec is also a good weekend, and may have longer park hours than 12-14 Dec, or maybe not. It's hard to tell until you get closer.
Could you wait until Jan 09? from about 9 Jan to mid-Feb (whenever that value season ends - I don't know those dates) would also be a good bet for low crowds. Avoid Martin Luther King weekend, though.
Whenever you decide to go, have a Magical Time.