I feel guilty that I haven't posted in this thread yet, as I have been visiting Chester for 50 years and taking photos there for almost as long.
The best way to get good photos at Chester is to use your eyes and your legs equally: it's such a big zoo with such a range of animals that if the enclosure you're looking at doesn't give much chance of a good photo, you can always move on until you find an interesting animal in the right place to get a good shot. If nothing is happening with the giant otters, try the black vultures or the spoonbills on their nests, or the penguins or the tigers and so on.
I agree about visiting the orangs early, but don't forget to call back later because sometimes they sit in the sun at the edge of the water barrier. Some of my other favourite targets are the blue-throated macaws and the red-tailed amazons that share their aviary, the capuchins in their outdoor enclosure, the tuataras (I think they come further out of their holes in the afternoon), the Indian rhinos, the vicuna (particularly the babies, which look like fluffy versions of Bambi) and the birds in the Tsavo aviary (where the light is best late in the afternoon). I haven't had much luck with the bears or the mandrills or the miniature monkeys in recent visits, but I'll keep checking because sooner or later I know I'll get an opportunity for some good shots of them.
Good hunting
Alan