Can We Make It?

I would not risk trying to get to the cruise departure port of the same day of your cruise. You won't miss anything from your RS tour on the last morning of your tour other than breakfast. I do see that flight schedules for this route don't seem to be very friendly. You would miss the farewell dinner, which is often quite nice, but I would be tempted to fly out the day earlier.

I have been planning on that option but really hate to miss the dinner and possibly the Borghese Gallery. I have been wanting to go on a RS tour for years and this is our first!

Better safe than sorry, but perhaps I should gamble!

I don't suppose you'll be traveling with carry-on only?
If you chance this, taxi is the only way I would do it.

I guess another question is: What is the first port of call for the cruise? If things go sideways, can you be sure of catching up with the ship there?

We will be traveling with carry on only so that helps. I would also pay extra so we were positioned right next to the aircraft door.

No, I wouldn’t take the risk. I’d take the earlier flight. Or preferably fly out the night before the cruise. Even if your flight arrives on time, you have 2.5 hours to exit the plane, go through immigration, collect any bags, get to your private transfer/taxi, drive about 45 minutes and get on board. What if there’s traffic, an accident, your private transfer driver is MIA, a bag is lost by the airline, there’s a long line at immigration, etc. My “what if” anxiety would be too great.

Boarding for the cruise is Noon until 4:00.

I have never been to this airport and don't know how long it would take to get off the plane with our carry ons, get to Immigration and then to wherever ground transportation departs.

Where is the boat's 1st stop after leaving Athens? Could you meet it there if your flight is late?

The final dinner is special, so missing it would be a sad thing.

google shows the trip from ATH to the harbor at 35-55 minutes, ( ~30 miles) so getting there by 3ish should not be a problem.(excluding some extraordinary circumstance)

As the flight from Rome does not entail any immigration process, you do not have to do anything but walk out the door to the taxi stand when you get to Athens

Just be sure the Tums are handy

Good luck!

Joe, I didn't stop to think there wouldn't be immigration to go through...hmmm.

The first port of call is Thessaloniki. Flights to there are $78 each plus we'd get stuck with a night's lodging there.

Your flight will come from Rome, and therefore will arrive in the Schengen area of ​​the airport. So there is no special immigration control when you arrive in the Schengen zone.
By taxi, the journey time between the airport and the port is about 45 minutes, (maximum 1 hour if there are heavy traffic jams.

So you will have at least 1h30 between the scheduled arrival of the flight and the departure of the taxi.
I think it's quite doable if the flight doesn't have an exceptional delay.

You can also book a taxi in advance with companies like welcomepickups (or other) a driver will be waiting for you holding a sign with your name on it.

google shows the trip from ATH to the harbor at 35-55 minutes, ( ~30
miles) so getting there by 3ish should not be a problem.(excluding
some extraordinary circumstance)

Just remember that Google maps tend to be very optimistic when it comes to travel times.

The first port of call is Thessaloniki.

In that case, the worst case scenario is that if you miss the ship, you take the train to Thessaloniki and board it there.

The port of Piraeus is huge (4 kilometers Between Gate A1 and Gate E1 ) so when you take a taxi, the driver will ask you to specify where in the port.
Inform the driver of the departure gate of your boat (if it is a Cruise Gate A, B or C or a ferry Gate E1 to E9), he will drop you at the right place.

I would book a taxi in advance. When we arrived at the airport there was a metro strike and the line for taxis was ridiculously long. We ended up taking a bus and moving back our scheduled tour.

Things like this are not that unusual in Greece and could seriously mess with your plans. (We also experienced a ferry strike in our two week visit.)