Call them direct. They have way more times than what shows through the Disney web. I tried booking online and the only available reservation time was 9:00. I called direct and had no problem getting a 6:00.
I also called them direct for our reservation for August (407-828-8739). They had no problem putting the reservation into their system even though it was for six months away. Also, the person I spoke to knew that you could not book decent times through the Disney Reservation system but did not explain why, she confirmed that she knew about it.