I don't know if anyone will read this at this stage but there is an ongoing discovery in ancient dna. Mainland Italy's genetic makeup changed drastically from the start of imperial Rome because of a massive, and I mean massive, influx of eastern mediterranean ancestry. These people came mostly in the form of Greek - speaking Anatolians and to a lesser extent Levantines. This shift is starting to be called the "east med shift" in ancient dna and the evidence is quite frankly astounding. Whatever reason, indentured servitude to become a Roman citizen, or any other reason, tons of eastern provincials migrated en masse to Italy in the early stages of Imperial Rome. Of course, places like Sicily already had greek speaking populations since the first Greek colonies on Italian and Sicilian shores. Just a funny anecdote considering the question above.

You are missing the largest one. That of eastern mediterraneans (Greek - speaking anatolians mostly) to mainland Italy from the start of imperial Rome.