Call them directly. I did that and pretty much had my choice on times. I even called the day before to change my time and they could get me pretty close to what I was looking for.
I had reservations for Sunday at 4 and called that day to get something later. The best they could do was 4:45. We decided to change to Monday and got 5 no problem. They were empty and excepting walk-ups.
Since they are not Disney owned, they are not giving Disney all their slots.
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