How would you guys recommend doing to get a great species list for a zoo without taking up too much time?
Get out your phone or camera and take a photo of every enclosure label, then go home and transcribe it later.
I'd second that, It becomes much easier to enjoy yourself while at the zoo, and you can worry about the species specifics and some of the harder to identify species once you reach home.
This is exactly what I do. It means quite a bit of work at a place like Fort Worth Zoo, as the Reptile House there has around 150 species! I take 150 photos of enclosure signs, plus dozens of photos of exhibits, and then painstakingly go through all the images that evening and type out a list. It's more fun than it sounds.
It's taken me three weeks and 1100 photos to go through Shedd aquarium, although only about 350 of those photos were of identification signage, the rest were of the fish for me to try to identify later! It is quite fun, though.