It's a busy week. The values and moderates are pretty much filled. The best thing is to hope for a cancellation or check with room consolidators.
You might want to check airline websites (no need to book airfare). I know that USAirVacations has room packages available at value resorts for your dates. So does SouthwestVacations. Of course, to do this you would have to cancel your reservation with Disney (wait for a refund) and book with the third party. Also, third party TAs may require full payment when you book and their cancellation policy may not be as generous as Disney's.
If you want to deal directly with Disney, keep checking and change your reservation by dropping dates. Some rooms may be available at the end of the week but not the beginning. Or visa versa. Then keep checking back for openings on the dates that you need until you have your entire week. The risk you run by doing this would be that you can't get all of the days that you need.
