I'm also in favour of this exchange, but I will say I was at Tierpark Hagenbeck a couple days ago and they were totally fine about re-entering the zoo. However, I may have just gotten lucky
They did accept us back in after failing to revisit the Tropenaquarium but the zoo was staffed by angry old men that day and they were muttering how it was not supposed to be like that...
The three you propose I would DEFINITELY go to if I had more time, and Stuttgart got SUPER close to getting into my plan. I'll save them for a second trip, should I get the chance. I decided to opt for Hamburg and Duisburg to get a chance to see walruses, manatees, bottlenose dolphins, Tasmanian devils, rare arctic seabirds and mandrills.
Mandrills are a very interesting addition to this list
I will definitely keep these times in mind; I plan to spend as long in these zoos as possible, with the possibility of revisiting areas if the first time wasn't too successful. Too bad they only allow you to visit the aqua-terrariums once... it seems a bit daft to me, to tell you the truth; imagine a reptile is impossible to photograph in the morning, but has shifted to a perfect pose in the afternoon or vice versa; people are being denied that second chance here!
Annoying indeed, especially as in Cologne it wasn't an issue until 2022.
Considering I'll be spending all day at these zoos, which route would you recommend I take through them? Like in the Berlin Zoo, if I start at the Elefantentor, would you start with the primate pavilion and leave the cats for last, or vice versa?
As for recommended routes:
Köln Zoo: do the aquarium + terrarium first and start with the terrarium, so you can visit it twice before leaving the building. I then always move to the Hippodom first and in general keep left on my loop through the zoo. Be sure to check all the ponds and other water features, rare ducks are everywhere!
Frankfurt Zoo: I normally visit the cat house first and then loop back to see the duikers + giraffe house and make my way to the great ape house. Then by 10 am the Grzimek house and Exotarium (aquarium+terrarium building) open. Always visit the Grzimek house first as it might still have the lights on and there are no crowds yet. Only then do the Exotarium. People in Frankfurt seem to visit the zoo quite late, so it becomes very crowded later in the day, but the early hours are quite empty.
Leipzig Zoo: Make a beeline for the aquarium and then Gondwanaland + the old bird house next to the sea lions & the pangolins in the elephant house basement. If you happen to arrive a bit later, visit the zoo clockwise, so you visit against the stream and you will have the first and last part of your visit without the crowds (and crowded it gets!). They follow a somewhat annoying fixed route with only a few shortcuts, so be aware of that

.
Zoo-Aquarium Berlin: Normally I start at the Lions gate and then move via the elephants to the primate & carnivore houses and then I visit the aquarium. Those parts get most crowded. After that you just find your way through the zoo as it suits you
Tierpark Berlin: when entering near the bisons, I tend to turn right and via the bears & gulls visit the Alfred Brehm house first and then move to the monkey house & mountain zone. But crowds in most areas aren't a problem here. Be sure not to miss some of the rarer species, the map isn't too helpful for that, so if you have specific animals to see, ask it here...
Tierpark Hagenbeck: My advice would be to enter the Tierpark first and move past the old entrance and the base of the African panorama straight to the Eismeer. It does get crowded in there, but early morning you should have the walruses and all the big underwater windows for yourself, which is magical. I found that the Tropen-Aquarium didn't get too crowded, even mid-day, probably because you have to pay big bucks to enter.
- Duisburg Zoo: First visit Rio Negro (manatees) & the aquarium and then you can make your way to the koalas and Tasmanian devils. The bottlenose dolphins might only be visible during the show, and if they are visible outside of the shows, it is only from a distance.