Rome/Cruise and ?

Well, Milan, Venice and even cities in Switzerland or France are closer to Genoa than Rome. But you can check for internal flights from Rome to Genoa if you have your heart set on Rome.
This day and age of cheap European flights, of course 2 weeks in Greece is doable....but given that you appear to prefer slower travel, and you are in Italy already, do as considered, and see another area of Italy.
Following year do a cruise of Greece and the Adriatic followed by Greece land time 😊
Additional info. Amalfi Coast is lovely, but takes some time to get there from Rome - depending on where you want home base to be. To get to Genoa from there could take a full day. Even from Rome it is 4-6 hours travel time and needs the pre and post travel time considerations.
Of course, it is always nice to have a direct flight from home (not something I have the luxury of), but looking at flights that may have one stop could get you closer to your ultimate destinations. For example, a multi-city (or 'open-jaw') flight may be better. Fly to Naples and home from Milan. The difference in price may make up for the costs for ground transport and the time involved to get from a perceived 'convenient' airport to where you actually want to go. With this plan, however, you still would need to get from Naples or Amalfi Coast to Genoa. These most likely would be on a separate ticket and you can do it by flying.
Whereever you end up, you would benefit from being in Genoa the day before your cruise leaves to hedge on the side of caution in the event of train strikes (which Italy does frequently enough to be a consideration) or just 'life glitches'.
I might suggest to push through all the way to Amalfi Coast upon arrival, even if it means hiring private driver from Naples to XXX and end in Naples, which would cut off some travel time. Tough it looks tidy and close on a map, Amalfi Coast is a bit of a backwater when it comes to public transport.
I use something line Rome2rio website to plot distance travel options. They are a first layer planning site, but give you options of what providers to dig deeper into.

If you go to Greece, you would likely have to fly within Europe. You may find cheap tickets, but a lot of those flights charge extra for luggage.

Flying into Rome would be great, it is my favorite European city. Much history, ancient as well as the amazing Vatican with St. Peter's and the Sistine Chapel.
Also, you can move north after 4-5 days in Rome. Florence is wonderful, and 3 days there would be great, then on to Genoa, perhaps stopping in Pisa and CT.

Further, the website cruise critic.com is a great resource for planning your travel connected with your cruise. Join the website and you can find a roll call for your cruise. Many people solicit for private tours that are cheaper than the ship's excursions.

We cruise a lot, usually doing a land trip in conjunction with the cruise.

Since you have already spent a month in Tuscany, Florence, etc I can understand the interest in further south, but have you considered even further north than you were before? Consider Nice or the French Riviera instead of Amalfi Coast? Turin, Milan, maybe even into Provence, even though you will be hitting Marseille on your cruise. Really, given that you most likely need to spend a day to get to Genoa from 'wherever', the world's your oyster on where you spend your 10+ days beforehand. It all depends on how much internal travel you want to do (and I guess, the luggage question above).