My understanding is that modern Greek is a 19th century construction, not a 1st century survival. It resembles Classical dialects because it was designed to.
Your understanding is entirely wrong, then
Any highschooler here can read the NT from the original Attic Greek, cause it is pretty much all part of the current language. You may confuse things with Israel's resurrection of ancient language to substitute the yiddish one developed entirely by the european jewish diaspora.
You might also (not sure, cause it is not that known outside of this country for non-linguists) refer to the Kathareuousa vs Demotike affair, which ended in the late 1960s with the pitiful establishment of the latter, as a supposedly "more accessible" version of Greek. In reality the language is near enough Byzantine documents from more than 1000 years ago, to allow most to read those with some second-guessing or a dictionary of obsolete terms.
Of course if one compares current Greek to Homeric Greek...it is a different issue, cause then there are many more changes, including grammatical changes. For example i was never good in "ancient Greek" in highschool, and it was quite different grammatically, despite many elements remaining in current Greek (the gospel's attic Greek was very very simple, though, i suppose so as to allow more people to read it).