Hey there!
Congratulations on your upcoming honeymoon! It sounds like you and your fiancé have different travel preferences, but a cruise might be a good compromise for a stress-free and relaxing honeymoon. Europe is an amazing destination, and I think starting in Rome and ending in Venice is a great itinerary.
As for your questions:
For Italy and Greece, I would recommend checking out cruise lines like Royal Caribbean, Norwegian, and Celebrity. They all have itineraries that stop in Italy and Greece, and some even offer overnights in Greek Islands like Santorini or Mykonos.
While it's true that you might miss out on some local dining experiences on a cruise, most ships have plenty of dining options that offer fresh and authentic cuisine. Plus, you can always explore local restaurants during your port stops.
Adding extra days to your trip should be fairly easy, especially if you're starting and ending in major cities like Rome and Venice. Just make sure to check with your cruise line and hotel to ensure availability.
I haven't done a similar trip myself, but some pros of cruising include convenience, all-inclusive pricing, and the opportunity to visit multiple destinations without having to pack and unpack. Cons might include a lack of time in each port and potential crowds at popular tourist spots.
As for a personalized honeymoon gift, have you considered a custom photo album or a personalized travel map to document your trip and memories? Just an idea!
Hope this helps and happy planning!