My books on ancient Greece are pretty old. And they have have the same explanation for Doric vs. Ionic ethnicity/history.
Are there any archaeological evidence for a Dorian invasion?
There are no conclusive archaeological evidence for the event, or series of events that's today known as the Dorian invasion. Even the name of the theory itself is problematic, as it suggests a violent and perhaps swift large scale event, an oft used alternative1 is "Dorian migration", while in Greek the event is known as "Κάθοδος των Δωριέων", the descent of the Dorians, with the term "descent" suggesting a migratory movement from North to South, without necessarily suggesting an invasion or occupation.
The commonly quoted archaeological evidence that suggest a violent event is the destruction of the Mycenaean palaces, possibly by invaders. Linear B disappears after the destruction of the palaces, further suggesting that the destruction was the result of outside forces. However it has been argued that the series of Linear B tablets found in Pylos attribute the destruction to the Sea Peoples, and not Dorians2:
As for literary evidence, Herodotus in passage 56 of the first book (Κλειώ) of his Ιστορίαι (Histories) writes:
And on passage 27 of the ninth book (Καλλιόπη) he mentions:
The events Herodotus describes and the legend of the Return of the Heracleidae3 seem to suggest that a violent large scale event that today would be described as an invasion, and perhaps occupation, did take place in the general area and general timeframe the invasion of the Dorians is commonly placed.
However it should be noted that Herodotus is not the most trustworthy of historians, and today perhaps he wouldn't even qualify as a historian. Plutarch openly criticized the sometimes fictitious nature of the Histories in On the Malice of Herodotus, and Aristophanes mocked his recount of The Peloponnesian War in The Acharnians.
Without conclusive archaeological evidence, and with all literary evidence being a blend of history, politics, biased personal accounts, mythology, and perhaps outright lies, the concept of a Dorian invasion is still more of a theory, than fact. The period between 1200BC and 750BC is commonly called the Greek Dark Ages, and I'm afraid the name was aptly chosen.
1 Thomas Keightley used "migration" on Outlines of history and then switched to "invasion" on the The Mythology of Ancient Greece and Italy.
From my readings and understandings if this period Dorian migration is more sufficient and during this period there were several seemed issues regarding invasion but these can be attributed to illyrian and Phrygian movements as well as the still unknown sea people. There had been archaeological evidence which shows fortification of ethnic greeks throughout aetolia attica and northern mountainous parts of Greece such as epirus and Thessaly but not three same level of fortification throughout the pelloponnese leaving those to assume movement from the north. I would consider Dorian migration party of this upheaval from other external ethnos pissing down into the Balkans as they were moving towards kin like proto greeks away from external groups. This would also work towards Macedonian statements of constant war with paeonians, illyrians, Thracians as this was most prevalent in their history from 700~500's bc as their kingdom was constantly threatened from these groups and did not seen too stabilize till after liberation from the Persians in the 500's. Now i am not an authority as i am not a scholar in these areas but this is what i have learned as part of my formal education. But thus seems to be a rational conclusion to this period of Greek dark ages, seeing the first contact and arrival of new external forces from the north onto proto Greek and Greek peoples.