Was the Greek population in western Asia Minor continuous from Byzantium, or did it migrate back to Asia Minor in Ottoman times?

Motivated by discussion with Dimitra Triantafyllidou at Nick Nicholas’ answer to What are major languages which declined/extinct during Turkification of Anatolia?

Citing from discussion there:

The received wisdom, from:

• Vryonis, Speros, Jr. The Decline of Medieval Hellenism in Asia Minor and the Process of Islamization from the Eleventh through the Fifteenth Century. Berkeley: University of California Press, 1971.

is that the bulk of Asia Minor was islamised and turkicised relatively quickly after the movement of the Turks into the region.

It seems that the substantial Greek populations in the Western Asia Minor coast date from Ottoman times, with Greeks settling the coast from the nearby islands. The dialects of the coast are certainly close to those of the Aegean islands. Dawkins concurs, speaking of both settlement from the islands, and a wave of migration out of Greece in the 18th century.

• Dawkins, Richard McGillivray. 1916. Modern Greek in Asia Minor; a study of the dialects of Siĺli, Cappadocia and Phárasa, with grammar, texts, translations and glossary. Cambridge: Cambridge University Press.

We know that Bithynia was resettled by both Greeks (from Epirus) and Bulgarians in the 1500s–1600s. In fact, there was even a Tsakonian colony on the mouth of the Gönen river, which probably dates from the 1700s.