Bonjour Jessica,
Having traveled with children of your son's age, I totally get it! Timing of reservations can be KEY to a successful evening with full tummies and happy moods. My best advice to you is to continue to check the site daily for
Advanced Dining Reservations at Be Our Guest. You'd be surprised to see the occasional reservation open up as guests change their travel itineraries.
Because of the immense popularity of Be Our Guest, my other suggestion is to dine for quick service lunch. Although always subject to change, currently only at lunch are guests allowed to choose one of three dining rooms adorned with the most ornate architecture and detail. There is also significant savings dining at lunch versus dinner. Check the unofficial site allears.net to view and compare the menus and prices.
If you decide to arrive for lunch, I'd suggest lining up as soon as the queue opens at 10:30 a.m. If you arrive a bit later, don't be too concerned with a very long line as the dining rooms can accommodate over 500 guests at a time.
Wishing you the most MAGICAL experience, Jessica, and visit us again with other questions!
Bon Appetit!
Sherri