I had this happen with building droids. The site had dates and it said no times available. One day, it seems like it finally synced and there were all kinds of times available.
Whether that applies to fireworks? I have no idea. They probably sell out very quickly. Also, since it is an "Enchanted Extra," the times are not always posted at 6 am like other reservations. They drop when they drop. I checked for May 25 at 3 pm one day and they were not open. Sometime between 3 pm and 5 pm it opened and it said no times available. I wish they would just have the times go at 6 like everything else. I can't be on my computer all day waiting on it.
I was told by a dining representative when the venue is ready to reserve, they just put them out there. My suggestion to them was when they are ready to reserve, hold off until 6 am the next day.
Keep going to the site and trying, maybe a cancelation will happen for you. Keep the faith! Maybe book something else that is special for that day while you wait?