I agree with you Chief that the train is an easy way to get around , but not with large amounts of luggage it gets pretty full. The Hotel Traiano offers airport pickup at much less than you quoted, it cost us only 90 euros last year.
I arranged a post cruise pick up by limo using an Italian agency I have used before and even that was only 150 euros.
We will be doing the same again next year after being bumped off the Liberty from Dover and are now booked on the Dream on 21st Sept