I have not been to InSync, but it looks like they are northeast of the Dallas Metroplex. A similar place that is northwest is this one:
Home.
Dallas and Fort Worth both have cheetahs but you live near the best cheetah exhibit in the country at Phoenix Zoo, so these exhibits will pale in comparison (though both are decent). The one at Fort Worth is open viewing from a raised boardwalk that extends into the exhibit. The one at Dallas is through glass (though in my opinion the more visually appealing of the two).
Dallas Zoo has lions (next to cheetahs) and Sumatran and/or Malayan tigers on the other side of the zoo in an outstanding exhibit. They used to have caracals that could only be viewed from the monorail - not sure if those are still there. Sadly that is the extent of the cat collection in an otherwise brilliant zoo - the best zoo in the southwest IMO.
Fort Worth Zoo (in addition to cheetahs) has lions in an average exhibit and neighboring exhibits with white hybrid tigers and Malayan tigers. The Texas Wild section has pumas and jaguars and an alternating bobcat/ocelot, all in exhibits that are a bit too small (the puma exhibit is way too small).
As you likely know, Fossil Rim is one of the main cheetah breeding centers for all AZA zoos. The drive through goes onto a hill with five or six very large enclosures (perhaps one acre each). For an added fee (book ahead) you can do a tour of the Intensive Management Area, which includes the off exhibit cheetah breeding area (plus carnivores you cannot see on the regular self drive, such as maned wolf and Mexican wolf - they also recently added black footed cat, though I do not know if they show those on the tour). I did this tour a few years ago with my cousin and it was well worth it. Fossil Rim is a favorite of both me and my cousin (and featured in my book on southwest zoos) and I would STRONGLY recommend fitting it in.
Even though I made several trips to Texas I never visited Dallas World Aquarium. ZooChat members rate it highly for the rarities, but except for crocodiles I think there is nothing on your wish list to justify a visit. I have not visited for this reason but also because I have the impression many exhibits are too small and I do not want to support a zoo in a warehouse.