Are you sure it’s booked up? I’m sure that’s a busy time (I think something’s opening around then?? Maybe?? ) BUT… the past few months, the calendar dates have turned blue/became clickable but still showed no availability. Then a few days later, the availability opens up. So if it just turned blue on the calendar, that could be the issue.
This happened to me for my June EMM date. The day the calendar date turned blue and was clickable, it said no availability. I called Disney and the CM said Oh, well it must already be full. I pressed her to check if it was full and she said Oh wow! You’re right. It shows 0 bookings. Sure enough, 24 hours later I was able to book it. If i were you, I would call and ask them to really look if it’s full (not just assume because they can’t book it themselves). If it’s not, check back every day until availability is released.