This is calling out for experimental archaeologists to make the best possible front surface reflections they can from polished copper, bronze, steel, obsidian, glass. The Romans had metallised glass. They knew how to roast glass. They may well have known how to vaporise metal onto glass.
The state of the reflecting surface with 2ky of corrosion does not match even looking at your reflections in water.
There's this tendency to assume ancient = primitive, but these were skilled artisans with deep material knowledge
Agreed. I imagine that obsidian surface must have been as polished as my smartphone screen in its prime, and probably as useful as a mirror (screen turned off). I am not sure of the flatness they were able to achieve though, so the reflection might not have been perfect. In theory a perfectly flat surface is achievable if they used the same tool to polish multiple mirrors at the same time!