As you know, Stoics are cosmopolitan, so you have the right claim on Epictetus.

I don’t think the debate is about what to call it, it’s about the nature of the field. Even so, Mediterranean studies is still a bit parochial, and inaccurate (the classics do not include texts from Egypt, for instance, and for good reasons, very different cultures).

As for building up something new, Padilla seems awfully vague about what that would look like.