I am not aware of how tied their idiom is to ancient doric. Look for a lot of "a"s in place of the standard "e"s
That's what my teacher for Greek at secundary school also said: more epsilon's and eta's.
As anecdote
I skipped Greek when going from the third to the fourth class because I had to make a choice between Greek and Math II (vectors, matrix, statistics) and I really wanted to have all aimed at natural sciences when getting my school diploma.
So lazy or minmax as I am, I had not put that much effort anymore in getting good grades that year for Greek. So one of the last lessons I got a oral exam which would determine whether I would pass at all to the next year, and that teacher, being a real nice guy in general, asked me to sit on the chair for oral exams in front of the class, the roasting chair, the book on my lap.
I was prepared and could rattle up the homework for that day, some translations of in advance known pieces of texts, even upside down from the top of my head.
So he smiled for the effort, but even a max grade would not be enough by math to get that year's overall grade high enough... pfff... I was at his mercy already.
and then said: "It is not about Greek language, but about what you learned here on the classic culture of the Greek directly from their texts... so... what can you tell me about Greek culture ?"
And I had just read about that story of the Cyclops story of Odysseus which could come from dwarven elephant skulls found recently on Cyprus.
So I started with telling that the name of Cyprus was coming from the Greek Kupros, meaning copper, because of the rich copper veins there and then moved to the Odysseus story which was new to him.
Yesss
He even told straight away... you passed !
A year later, to pass to the 5th class, still lazy, I skipped Latin again because of limitation of max subjects.
During my time at secondary a new school education law was implemented, massive effects and called the Mammoth Law, reducing the knowledge level tremendously of secondary school gymnasiums in order to make education more accessable.... but adding subjects on top was forbidden. Our rector violated the rules where he could and found mostly good teachers.
In order to have full natural science package I even had to skip geography and history in the 5th and 6th class
Anyway, the same as with Greek happened with Latin... the teacher told me later, happily in private and not in front of the class, that the only reason I passed Latin with high enough grade was that I had sung so beautifully in my first year as soprano in the school choir