It shouldn’t be that crowded, its actually a great time to visit! The beginning of the month (first or second week) is always better. The weekdays are usually better, too. You may want to plan your arrival in the middle of the week (on a Tuesday or Wednesday). This way, your off days in the middle of your vacation are during the weekend. This way, you can take a day off to relax at the resort or a Disney Waterpark and still beat the crowds of the Florida locals visiting on the weekend.
Disney has offered a wonderful discount package in September called Stay, Play & Dine or Magic Your Way Package plus Free Dining. This discount package has been offered for several years, so there is a good chance it will be offered next year. This is one of the best deals on a Disney World vacation! Be sure to watch for this promotion, it usually comes available in early May.