Thanks for the recommendation, Diplomatico.
That is a good point about the cashback - we are definitely trying to spend as little as possible. We obviously did not want to go to Italy in the dead of summer during high tourist season. But, alas this is what we do for love and we'll make the best of it.
Unfortunately, the Norwegian flight is just one way to Rome. We would still have to fly back to NYC from either Verona, Venice or Milan.