I have studied Latin at the university level and also some Greek, especially from the historical linguistic point of view.

I truly understand that the ancient pronunciation sounds bad to your ears! All those "mistakes" that you mentioned are exactly the ways that Greek pronunciation has changed over the thousands (!) of years. If you look closely, it is as if the writing system is made for the old language, which is the case. The modern pronunciation drifts further apart from what is written. Historical linguistics is quite interesting once you get into it.

I recommend the following books, although both quite technical in the linguistic sense:

Allen, Vox Graeca: The Pronunciation of Classical Greek 3rd Edition (Cambridge University Press 1987)

Horrocks, Greek: A History of the Language and its Speakers, 2nd Edition (Wiley-Blackwell 2010)