Jason
You really need to get it clear in your mind that 'n' does NOT invalidate invariance, which was only ever of.. "light in a vacuum".
i.e. In the 1950's Feynman was in awe of Lena Hau slowing light to 35mph in BEC. It never invalidated constancy of 'c'. The bit you keep forgetting is that the 35mph in BEC is constant whether the BEC was in her lab, on a train, a plane, or the space station. Light arriving from any observers rest frame will simply change speed both; A to comply with the media's 'n', and B to comply with any relative motion of that medium wrt the rest frame. The evidence of the Doppler shift proves it has done both.
You're not alone in repeatedly forgetting that, which makes nonsense, anomaly and paradox of perfectly consistent physical results. It seems our brains are simply not well developed enough to easily hold and apply two variables at once. That's why the 'elephant in the room' is not visible to most humans for more than perhaps a few minutes at a time. Once we've thought it through repeatedly and our brains have got used to applying it, it all becomes very familiar and simple. But it won't happen without effort, and being told how it works first. I's no wonder Einstein couldn't see it.
The speed of light in a vacuum is absolutely constant LOCALLY, in ALL regions of space, which is why it is constant to ALL observers, in all inertial frames.
I really hope you can do this as it's a revelation.
Peter