My books on ancient Greece are pretty old. And they have have the same explanation for Doric vs. Ionic ethnicity/history.
Is 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:
Evidence on the Linear B tablets from the Mycenaean kingdom of Pylos describing the dispatch of rowers and watchers to the coast, for instance, may well date to the time that the Egyptian pharaoh was expecting the arrival of foes
As for literary evidence, Herodotus in passage 56 of the first book (Κλειώ) of his Ιστορίαι (Histories) writes:
Of all the answers that had reached him, this pleased him far the best, for it seemed incredible that a mule should ever come to be king of the Medes, and so he concluded that the sovereignty would never depart from himself or his seed after him. Afterwards he turned his thoughts to the alliance which he had been recommended to contract, and sought to ascertain by inquiry which was the most powerful of the Grecian states. His inquiries pointed out to him two states as pre-eminent above the rest. These were the Lacedaemonians and the Athenians, the former of Doric, the latter of Ionic blood. And indeed these two nations had held from very early times the most distinguished place in Greece, the one being a Pelasgic, the other a Hellenic people, and the one having never quitted its original seats, while the other had been excessively migratory; for during the reign of Deucalion, Phthiôtis was the country in which the Hellenes dwelt, but under Dorus, the son of Hellen, they moved to the tract at the base of Ossa and Olympus, which is called Histiaeotis; forced to retire from that region by the Cadmeians, they settled, under the name of Macedni, in the chain of Pindus. Hence they once more removed and came to Dryopis; and from Dryopis having entered the Peloponnese in this way, they became known as Dorians.
And on passage 27 of the ninth book (Καλλιόπη) he mentions:
Thus spake the Tegeans; and the Athenians made reply as follows:- "We are not ignorant that our forces were gathered here, not for the purpose of speech-making, but for battle against the barbarian. Yet as the Tegeans have been pleased to bring into debate the exploits performed by our two nations, alike in carlier and in later times, we have no choice but to set before you the grounds on which we claim it as our heritage, deserved by our unchanging bravery, to be preferred above Arcadians. In the first place, then, those very Heraclidae, whose leader they boast to have slain at the Isthmus, and whom the other Greeks would not receive when they asked a refuge from the bondage wherewith they were threatened by the people of Mycinae, were given a shelter by us; and we brought down the insolence of Eurystheus, and helped to gain the victory over those who were at that time lords of the Peloponnese. Again, when the Argives led their troops with Polynices against Thebes, and were slain and refused burial, it is our boast that we went out against the Cadmeians, recovered the bodies, and buried them at Eleusis in our own territory. Another noble deed of ours was that against the Amazons, when they came from their seats upon the Thermodon, and poured their hosts into Attica; and in the Trojan war too we were not a whit behind any of the Greeks. But what boots it to speak of these ancient matters? A nation which was brave in those days might have grown cowardly since, and a nation of cowards then might now be valiant. Enough therefore of our ancient achievements. Had we performed no other exploit than that at Marathon - though in truth we have performed exploits as many and as noble as any of the Greeks - yet had we performed no other, we should deserve this privilege, and many a one beside. There we stood alone, and singly fought with the Persians; nay, and venturing on so dangerous a cast, we overcame the enemy, and conquered on that day forty and six nations! Does not this one achievement suffice to make good our title to the post we claim? Nevertheless, Lacedaemonians, as to strive concerning place at such a time as this is not right, we are ready to do as ye command, and to take our station at whatever part of the line, and face whatever nation ye think most expedient. Wheresoever ye place us, 'twill be our endeavour to behave as brave men. Only declare your will, and we shall at once obey you."
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.
2 The Trojan War, Carol G. Thomas and Craig Conant, via Wikipedia.
3 The return of the exiled descendants of Heracles to the Peloponnese in order to (forcefully) claim the possessions they lost when expelled.
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.