Strawberryfields,
just go ahead and apply for an ID, you will need your EU passport to get a Codice Fiscale (the italian equivalent of the Social Security Number) and then a local address to register your domicile (a friends place will work).
They supposably do a background check on you but to be honest I seriously doubt it's that thorough as some like to describe it.
I was told by someone in the know that many of the non-EU baggage handlers that work in Italian airports in such great numbers are very often let airside without ever even receiving any clearance from their countries of origin.
On top of that ,according to the Italian law, your criminal record can be cleared upon request after 3 years have elapsed since your conviction in the case of minor crimes, allowing you full citizen rights (and an airside ID is definitely included).
Bear in mind that a crime committed abroad, in order to be so defined by the Italian judicial system, has to be considered as such also by the Italian criminal law otherwise it's just not a crime.