I think that can be mitigated in three ways: our understanding of inflation is flawed, there were more "nucleation" sites where our universe came to be, and the

I think that can be mitigated in three ways: our understanding of inflation is flawed, there were more "nucleation" sites where our universe came to be, and there are the already theorized baryonic acoustic oscillations that could introduce heterogeneity in the universe. Maybe is a combination of these, maybe something else. If nothing else, the uniformity is less probable than a mass distribution with variance (unless there is a phenomenon like inflation that smoothen things out, but also that was introduced to explain the assumption of a homogeneous universe). I concede that explaining the little variance in the CMB with our current understanding is hard when dropping homogeneity assumption however.