Just to add to what you said, the part of the Bronze Age collapse that was specific to Greece has been dubbed, the "Dorian Invasion".[0]
After the Dorian Invasion, the culture and languages/dialects in Greece were replaced by those prevalent in Classical Greece, the era of Greece most people think of when referring to "Ancient Greece".
Note, you should look at the Dorian Invasion like the PIE invasion—metaphorical. So it's visible via the archaeological record, but it's not that there was conquest so much as deep change where the Dorian culture clearly spreads over time.
Although conquest could be one such way of spreading culture, it's generally more by intermarriage than displacement (e.g. see the saxon and normandy invasions of britain or the romanization of gaul).
I'm under the impression that there was widespread democide during and after the Norman Conquest, particularly with the goal of eliminating the anglo-saxon nobility and aristocracy.
That is true, particularly in England. However the aristocracy mostly fled to other parts of Britain and Scandinavia; the Saxons certainly remained in force in the labor class and in the genetic pool. Of course, this is less true in England than Wales, Ireland, and Scotland, but saxony was not forgotten, English remained Germanic, and it would take many centuries until the Norman linguistic influence trickled down to the general populace. To this day you sound upper class if you stick to French (Latinate) derived vocabulary.
My point being: the pre Dorian culture remained in Greece as well. The Mycenaeac influence was still visible in the literature of the day as a distinct culture; there was no clear attempt to impose a foreign culture by violence or other aggressive means. Or at least no evidence. Of course, we might know more if we ever get Linear B, but who knows if we ever will.
This is all a very long winded way of saying "invasion" doesn't ever really capture the subtleties of cultural diffusion. Ghengis conquered much of the Middle East, but the resulting cultural change was both more visible in places Ghengis never saw such as Western Europe and it was driven more by trade than by direct imposition.
"Ventris was able to show, ever more clearly over the months that ensued, that the language behind the script was Greek – in his own words “a difficult and archaic Greek, but Greek nevertheless”."
Proto Indo-Europeans. The language they're believed to have spoken is the common ancestor of most European languages (eg. Latin, German) and Hindi. This invasion may have been more of a linguistic and cultural spread by imitation than people of one ethnicity actually displacing another. Doubtless there's some of both.
You should definitely read the book -- one theory the author challenges is the idea that the Dorian invasion was the proximate cause of the Greek Dark Ages. Instead, he finds evidence that the Dorians were moving in prior to the Dark Ages; they were more opportunists than invaders, taking advantage of the collapse rather than causing it.
The Foundation series by Asimov talk about the Foundation, that aimed to hasten and then control a still inevitable collapse, and ensure itself would be the replacement culture.
Al Qaeda, that can mean "The Foundation" in Arabic, is speculated to have this aim too, using immigration, intermarriage, and dragging western civilization in a extended unpayable war with the same idea: hasten the inevitable collapse, and be ready to rebuild and replace from the ashes. (And ISIS is an impatient Al Qaeda, and wants to trigger a total war, to overextend western countries even faster, and cause a refugee-driven diaspora)
Just to add to what you said, the part of the Bronze Age collapse that was specific to Greece has been dubbed, the "Dorian Invasion".[0]
After the Dorian Invasion, the culture and languages/dialects in Greece were replaced by those prevalent in Classical Greece, the era of Greece most people think of when referring to "Ancient Greece".
0. https://en.wikipedia.org/wiki/Dorian_invasion