But I also technically have dual nationality, because of a quirk of Italian law. So could I be president?
Might be you would have to drop your Italian citizenship if that is the case. Don’t know.
No you don't. There is a big difference between technical and actual. As it currently stands you have no dual nationality and to secure it would require legal action on your part to take advantage of any such quirk.
American law trumps foreign wrt life in American so you would be eligible having no allegiance to another power. Italy’s claim on you outside of Italy is null.
Get that campaign going.