We know that the Greeks were vaguely aware that a aboriginal people existed before them. Could we make a definitive link between the invasion and their founding myth
The only way I can think to answer this question is to address the misconceptions bundled up into it. Let's make a list!
'Indo-European' doesn't work like that. 'Indo-European' is a name for a family of languages: it does not refer to states or ethnic groups. The idea of linking 'Indo-European' to race is one of the oldest tools in the ethnic nationalist playbook. People that talk about 'Indo-European people' don't usually intend to be racist, but, well, the idea is expressly based on an idea of ethnic nationalism. Language is one among many characteristics that an ethnic group can use to define itself, but there's no obligation for any ethnic group to do that, and there's no necessary link between language and ethnicity. There's definitely no implication about bloodlines or genetics.
Ancient Greeks weren't aware of an earlier aboriginal people. Some parts of Greece had legends that there had at some point been other ethnic groups there, such as the Pelasgians; other places like Athens and Thebes regarded their people as autochthonous, that is, the same ethnic group had always lived on the same land.
... and they may well have been right, to all intents and purposes. It's possible that an Indo-European language didn't arrive in what we now call Greece until the early 1000s BCE, and many placenames came from a non-Greek language or languages which were presumably spoken earlier, but that's well over a millennium before sources about Greek ethnic origins start popping up.
The Dorian invasion is a legend that was current among the classical Greeks. They regarded it as one among several migrations, in which several Greek ethnic groups moved from one part of Greece to another. The Dorians, for example, supposedly moved from central Greece to the southern Peloponnesos; the Achaians supposedly moved from Laconia and the Argolid to the northern Peloponnesos; some Aeolians supposedly moved from Thessaly into Boeotia, and others supposedly moved to the north-east Aegean Sea; and the Ionians supposedly moved from the northern Peloponnesos to the islands and to south-west Anatolia. The classical Greeks imagined these population movements as taking place around 300 years before the colonisation period. We'd call that around 1100 BCE, but I'd say it's a category error to treat that as the 'setting' of the migration legends in any way, because there's no way of checking to what extent the reality of 1100 BCE had anything to do with those legends.
You'll notice I mentioned five distinct migration legends in the above point: there are others too. They're all about people moving from one part of the Greek world to another. None of them is about anyone invading from outside the Greek world.
Not all Dorians shared the legend of the Dorian invasion. The Dorians of Argos, and the islands of the south and south-east Aegean, had at least two other distinct stories about how they got there, and they're incompatible with the Dorian invasion legend. The Dorians of Argos, for example, regarded themselves as autochthonous. The Dorians of Crete regarded themselves as having been colonised directly by a son of Doros from central Greece very early on in the chronology of Greek myth, long before the Dorian invasion supposedly took place.
If you want some reading on ancient Greek construction of ethnic groups within the greek world -- Dorians, Ionians, and so on -- this is not part of the popular perception of ancient Greece. As a result, what I have to recommend is pretty technical. You may find it worth poking your nose into anyway. My main recommendation would be two books by Jonathan Hall, Ethnic identity in Greek antiquity (1997) and Hellenicity (2002).
By contrast, something like Margalit Finkelberg's Greeks and pre-Greeks (2005), which argues that there genuinely was a Dorian migration, is informed much more by legend than by historical construction of ethnicity. She doesn't adequately address the question of what ethnicity is when it isn't determined by language, and she ignores the competing Dorian legends that I mentioned above. That doesn't necessarily mean her argument is all bogus, but I do think building history purely out of historical linguistics makes for a rather brittle argument -- it doesn't take much to make it shatter.
Edit: another recommendation: on language, you can't do better than Geoff Horrocks' book Greek. A history of the language and its speakers (2nd ed. 2010).