These are some of the selections that mention the ancient Morgeti to which my title alludes.
I would indeed distinguish between a Western Italic branch, which gave the Latins the Siculi and the Ausones/Opici, and this "Liguro-Sicanian" which I think included in the South the branch of the Oenotri (Morgeti, Sicani, Choni).
Peoples
The Sicani are reported by ancient authors to have been the first inhabitants of Sicily, at least among the historical ethnic groups. Thucydides and Diodorus say that the Sicani came from Iberia. Dionysus, quoting Hellanicus, says the Elymi (but likely he meant Sicani, since Elymi and Sicani merged later) were the first wave of Italian people to settle in Sicily. The second wave was that of the Siculi, which were Ausones escaping from the Iapygi. The same Dionysus says that among the Oenotri there were Siculi (possibly Sicani) and Morgeti.
Since King Morgezio's father was Enotrio, the Oenotri would refer to him, and the land that Morgezio's father conquered from the Ashkenazi, became known as Ausone during the father's reign, and then known as Morgezia in the son's reign. When the Iapygi invaded, the Siculi/Morgeti would have taken refuge near the site of the later Greek city of Morgantia, near Mount Etna in Sicily.