So I have some worlds with different physics, and need some way to explain it. As with other sci-fi, it would seem best to find something plausible but may be extremely unlikely or have negligible effect, and then exaggerate it.
The universe has many layers of emergent properties. So the current approach is to have a tiny change in some physical constant* (or multiple) which results in a new emergent property in that world which isn't in other worlds, or an emergent property which does exist in other worlds not being in that world. To facilitate this, it was decided each world would be its own galaxy, that way they wouldn't interfere much with each other and we wouldn't need to possibly reinvent astrophysics, and each of those galaxies could have one or more planets with intelligent life** in there somewhere. The distance between galaxies is a lot more than the distance within, so it makes sense that these constants seem invariant within a galaxy but could differ significantly between them.
So then using this route, the question now is, how is it possible that different galaxies can have slightly different physical constants? Or alternatively, if we have no way to explain it, is there evidence of physical constants being inconsistent in our universe? If so, it could be reasoned this scifi universe is just copying our universe.
As for the curvature of the universe, it seems it depends on how much mass there is, since the mass curves it. So that's for the entire universe, and using my limited knowledge of relativity, I'd guess it applies locally as well, there's just not the mass (or lack of mass) to cause significant curvature. Which means, for example, a very small isolated galaxy would have low density locally, and thus have locally very slightly hyperbolic space. I'm not so interested in calculating this curvature since I'll exaggerate it anyway, but rather whether this would be possible.
*Not a constant anymore
**Let's just ignore for now how to get between these worlds and how life would be both similar enough and develop at around the same time to facilitate intergalactic relations.