The 'deal you got' is NOT worth keeping. When you try to book something, there will be 'no availability.' You paid (or agreed to pay) $5,999 too much. We collectively think you got took. And 'in case you are not able to cancel', let this be lesson to you. The options: (1) You pay it off. Lots of TUGgers bought their first timeshare from a developer. Life goes on. (2) You make some kind of deal with the seller that they keep your $2,500 down payment in exchange for being let out of future payments. (3) You default. They suspend your membership. They turn you over for collection. The collector is silent for a few years, but when you apply for credit to buy a house/car/new credit card, you find a black mark from these weasels and it takes thousand$ to satisfy them and get your credit cleaned up.
I don't think that what you bought has any value. I believe it's a vacation club, not per se a resort. You've mentioned RCI Platinum a couple of times. RCI doesn't sell resort condos. It's an exchange company, and Platinum is a level of membership. You've 'bought 2 years of 'Last Calls' or Extra Vacations, with the ability (bogus as it is) to upgrade to larger units (there's that availability thing again) within 45 days before move in. I'm telling you it ain't gonna happen. You'll find 2nd or 3rd tier resorts on off- or shoulder season. You'll NEVER see a Hilton, Disney, or ANY other top level resort in prime time.
In my opinion, the best you can hope for here is what I described as option 2. Let them have the $2500 in exchange for your freedom.
But for now, you've sent a rescission letter. (though I don't believe you can rescind from a vacation club) The ball is in their court. Let them make the next move. You may or may not hear from them in the next week or so. You'll know you are making progress if the salesweasel tries to make contact.
Good luck and best wishes.
Jim