Also - factor in your plane tickets and their availability, which can be tight! I second the St Barths properties recommendation, but you will be hard pressed to maintain your budget (how many BRs do you need) - instead of St Barths look at St Martin/St Maarten and see if you can score on the French side. And I can reiterate that many places require 14 night minimums. Also look at Caymans, Dominican Republic, USVI, Tobago (maybe too far for you), Bahamas, and Mexico. The major villa companies' website will give you holiday avails, as I am sure you have found.

Good luck!

Here's one site -

http://www.caribbeanway.com/holiday-villas/home.asp