The region commonly refered to as "south Italy" could be as easily be described as "east Italy"

Yes, especially because the borders of pretty much any reasonable definition of it (the border of the former Kingdom of the Two Sicilies; the western border of “Neapolitan and related varieties” in this map; the western borders of present-day Abruzzo, Molise and Campania; the western borders of present-day Molise and Campania, to name the ones I can think of at the moment) run mostly north-to-south. There's no way someone from Termoli will identify as any less of a southerner than someone from Rome, which is geographically further south.