Logically speaking, it seems like it should work. Might be worth a call or visit to your local Italian Consulate office. They would have a definitive answer.

To help your cause, any way you can get the number of days you plan to spend in Italy under 90? For the just in case issues.

And if you are really worried, apply for a visa. They aren't too hard to get for IT, especially if you show them everything you are planning to do in terms of itinerary.