Are you sure about the uncertainty argument? As far as I know, there are even academics who sing the epic of Gilgamesh, despite the fact that Akkadian are more obscure than Greek or Latin.
At least in the Hellenistic period, the pronunciation of ancient Greek was similar to the modern version. An easy way, even for a non-expert, to notice this is the epigraphic and papyrological evidence.
Spelling mistakes increase dramatically, because the engravers and scribes, who weren't always very talented at grammar, couldn't discern the difference between υ, ι, η, ει, and oι or between ο and ω or between ε and αι.
Τhey sounded the same since the times of Seleucus, a fact that has created enormous problems for Greek pupils for 2.300 years.
Go to Facebook, follow Golden Dawn accounts who gloat about their links to Pericles and you will observe the exact same mistakes.
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