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how close is this to the theoretical maximum?

if we put mt. everest on a sperical cow, i mean on a planet with only ocean, how far could you see there? how far away could a second peak of the same height be, before it gets hidden by the curvature of the planet?

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If we have a 9 km mountain on an otherwise spherical planet (r=6371 km), the horizon would be 339 km away. With two mountains having a sightline between eachother the maximum theorethical distance doubles to 678 km.

Exactly.

And it could even be tweaked slightly with some favourable refraction.

Ah, well NASA left some mirrors on the surface of the moon so with some favorable reflection and infinite quality optics, you can theoretically see halfway around the world.

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