We did the Sunrise Safari in April, and we're doing it again in a few days. It was a really wonderful experience. We woke up really early in the am and checked in at the club lounge. From there we went down and boarded special buses that took us through a back way to AK. We got to see the employee entrance and buildings, the back-side of the savanna, and the huge cages/barns where the animals sleep at night.
Then we went out on the savanna and had a slow and leisurely ride through the regular ride. No silly ride story, no rushing. Just lots of information about the animals, their care. Plenty of time to take photos and ask questions.
Then we walked out of the ride area and to Pizzafari. There was a lovely buffet breakfast there, just for the people on the safari. By then the park was open.
Hope this helps!