The $206 AAA rate is good, but there is also a second AAA rate (promo code AAA123) which gives you the same $206 rate, plus you get a $50 resort credit, which can be used on food, beverages and recreational activities.
The Florida Resident and the Teacher rates are slightly better, at $199. However, there is no price difference between a two double-bed room and a king room...the room categories are based on location (Traditional, Resort View, Epcot View) and whether or not it has a balcony. It may just be the case that the Traditional king bed rooms are all booked, but I would call to verify that. In the past, I've been able to book a king room when calling the resort or SPG directly, even though no availability was showing up on-line.
You should also monitor the Starwood
Starpicks rates, which are released every Tuesday (except during holidays weeks, which means there may not be new rates released tomorrow). There have been times over the last few years, when the Starpicks rate was as low as $99 or $119 per night.
One thing I've learned with the S/D is to keep checking back, as their rates change often and it's not unheard of to snag a great deal within 4-6 weeks of your arrival date.
PS - definitely bookmark the
S/D Offers page, which pretty much covers all the bases as far as discounted rates and promotions go.