I think your chances are better than you think, and because of that I would not have "
any DVC" as my choice. Also, if HGVC exchanges via RCI points as well as weeks, your chances are even better.
I'd go for what you want most, and definitely would not list any resort where you'd be disappointed staying. I'd also make your range of dates as wide as you can -- a day or two one way or the other may make all the difference.
There is a tendency to assume that traditionally busy times for DVC will be impossible to get, but that is just not the case. Whenever some DVC owner exchanges out via RCI, that availability comes out of DVC's inventory and into RCI's.
As an example,
just yesterday I got a match for an OKW 2 bedroom for Dec 14-21, 2013. That was with Wyndham points exchanging through RCI Weeks. The OKW 2BR was the only resort and unit I requested, because we're hoping DD's BFF and her family will join us. But I used a wide range of acceptable dates between early October and 12/31.
If you'd asked people here, I'm sure most would have said that time period was completely impossible.
It's not.