Thank you everyone for your advice! I visited today, and quickly got through everything but the farmyard in 2.5 hours. This left me with enough time for repeat visits to the aviary (twice), pheasantry, museum of natural history, reptile house, primate forest, and Tasmanian devils.
I probably spent about an hour total in the natural history museum, and it is certainly an impressive exhibit. On my first walk through I was rushing to see everything, so honestly found the museum underwhelming, but on my second walk-through when able to really take my time I was blown away! The poison dart frog walk-through in particular is a genius exhibit, and it was a real treat to see a group of four golden poison dart frogs directly off the path, without any fogged-up glass separating them from visitors. I was also impressed by the sturgeon touch tank (they certainly didn't feel like I was expecting them to), and the salamander exhibit was visually impressive, despite the fact I only saw a single cave salamander and some sort of small tree frog that was unsigned. Upstairs, the venomous snake exhibits are certainly impressive, and I saw four elapids and thirteen viperids that I'd never seen before! The mixed-species rattlesnake species was particularly impressive, and the timber rattlesnake (I forget if this was in here or reptile house) had just finished shedding, so was absolutely gorgeous (I'm partial to any freshly-shed snake). Unfortunately, the flying snakes were a no-show (albeit slightly less frustrating of one than the Japanese giant salamanders at Detroit the day before), but almost every other venomous snake species was visible, and it really shows they put a lot of thought into the exhibits to make them great for the inhabitants but also great for visitors. All in all, this is probably my second favorite exhibit complex I've ever seen, only after Bronx's Congo Gorilla Forest. If it wasn't for the fact the signage leaves a lot to be desired in some sections, it'd likely be my favorite.
The aviary was also very impressive, and is my favorite bird-themed exhibit I'd ever seen (excluding Detroit's penguin center). Raggiana bird-of-paradise and Andean cock-of-the-rock were both highlights, as was the active, large group of emperor tamarins. The large flocks of starlings were also impressive to see, and in the African walk-through aviary the superb starlings and buffalo weavers were all very active and flying right near my head! The only part of the exhibit I wasn't a fan of was the Australian aviary, which just seemed to have wasted potential. Budgeriars, cockatiels, and Australian crested doves just seem like a waste of space compared to how many other impressive rare species are housed in the building. Perhaps the number one highlight of the day, however, were the kagus. On all three times through the building, the kagus were right near the front and would follow me around as I moved through the room. At many points they were also making their impressive displays, and it was so cool having the birds displaying and following me across the exhibit. I don't know if that's normal behavior for this pair of kagu or if there was something about me that triggered it, but it was really cool to see anyways and to have such a unique experience with a really unique bird.
Also bird-related, the Flamingo Key was a rather impressive aviary. I also felt it was a really smart move housing sea ducks in the penguin exhibit. While I didn't see any penguins outside, having underwater viewing for diving long-tailed ducks and spectacled eiders was a really unique experience that was also very neat to see. Another thing that surprised me was having three cinereous vulture cages (with the mixed-species waldrapp ibis one particularly impressive). I know plenty of zoos (including Toledo) have plenty of off-show bird areas for breeding that include multiple enclosures for the same species, actually showing three different vulture habitats on display was a neat touch, in my opinion.
The reptile house is definitely showing its age in some parts, and some of the tanks seemed on the small side, however in all fairness it'd be impossible to compete in exhibit quality with the Detroit's reptile conservation center I saw yesterday. It is still really cool to see older buildings with modern interiors, and this was an impressive, recurring theme at Toledo. The parts of the reptile house that impressed me the most, however, was getting to see a tuatara- really incredible animals that I saw for the first time today, and a saltwater crocodile- it surprised me just how big it was! The wall of Ranitomeya exhibits were also very nice, and it's cool to see a zoo highlight so many poison dart frog species so prominently.
On Tembo Trail, I was also impressed by the elephant barn. While the yards were average, the barn itself is probably the best elephant barn I've ever seen, which is certainly important for a northern zoo. There was an elephant keeper out at the yard when I walked through, so got to spend a few minutes learning about some of their elephant training techniques and how they manage their nutrition, which was nice.
While those were all very impressive parts of the zoo, oftentimes the best exhibits of their kind I've ever seen, there were also parts of this zoo that left a lot to be desired. While seeing the tiger cubs was absolutely adorable, the tiger exhibits were probably the smallest I've ever seen in an AZA zoo, which is a shame given they don't look like they're that old. It'd be nice to see in the future the zoo invest in some improvements to the tiger exhibit. A series of rotational tiger/snow leopard exhibits taking over the current dingo/tiger/snow leopard exhibits could be neat to see. The Arctic Encounter also left a lot to be desired. While the pinniped pool was nice, it was easily the weakest of four polar bear exhibits I saw this week. The Africa! section was also rather poor, with bad viewing angles and the bizarre inclusion of Bactrian camels.
Overall, however, I was very impressed by the Toledo Zoo- and it's now my third favorite zoo I've ever visited, after Bronx and Detroit. The best parts of the zoo were very impressive, and honestly if Arctic Encounter and Africa! simply weren't there, it'd likely rank as my second favorite due to how impressive the historic buildings are. Thanks for all the advice, I had a great visit!