I would think transliterating in cases like this should be based on classical Greek. That reveals much of the faux Greek logic to people who have learned the Greek alphabet for mathematics and physics but know nothing or little about modern Greek.
Not like I find it irrelevant how the text would be read in modern Greek. More like, I think that is taking one extra step towards complexity in analyzing the mess.
Kino's Travel
Painted by Rankei
English written in the Greek alphabet. The "Greek pi-omega symbol" (U+03D6) used for "v" and the "Greek small letter psi" (U+03C8) used for "y".
Transliterated
"Kino's Trapel
pendeth vps renkē"