There are a couple of TAXI/Limo providers that look through this website. Maybe one will send you a private message. Barring that, you should find plenty of taxis that would be willing to drive you to Rome from the port. Be prepared for a couple of hundred dollars of extra cost. If it were me, I would ask my private tour guide to push the time back. There are a multitude of tour operators outside the Vatican trying to sell tours. I can't believe yours wouldn't gladly push his tour back a half hour to 45 mins not to loose your business to another tour guide.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013