Post-Greece Tour to Santorini

I can recommend Lithies Traditional Homes which is located in Firostefani. Our stay there was fabulous! IMO there are way too many variables to say if a flight is "reliable". The night before a flight home, we always choose to stay in a hotel located in the departure city.

we don't know if the flight from Santorini to Athens is reliable

Santorini is an international airport served by plenty of airlines, and it's just as busy as any mid-sized European city airport. There’s no more and no less risk of your flight getting canceled there than anywhere else. It’s nothing like those other tiny island airports.
The two Greek companies Aegean and Sky Express which operate Santorini-Athens flights are very reliable, never had any problems with them.

So, it’s really up to you if you still want to play it safe and head back to Athens on September 28.

Regarding renting a car vs. taking a taxi:

We always rent cars when we visit the Greek islands. It’s 'better' for us because we love exploring the island at our own pace without depending on local public transit.

Just so you know, in Santorini, 2 taxi rides will cost you more than a full day's car rental. Taxis in Santorini don’t use meters, instead, they use "personal" flat rates that depend on the driver's mood and style.
A 15-minute one-way taxi ride from Thira to Oia range from €35 to €50 (which you could possibly negotiate ).

Note that there is an efficient bus network, that exact same trip Thira to Oia is only €1.80 on the KTEL bus.

We used a combination of rental car, taxis, and buses.

We had a taxis pick us up from airport and take us to Oia where we were staying.

We then hiked from Oia to Fira and used the bus to go back (very easy).

The next day we rented a car to explore the island. We were able to return the car at the ferry port which simplified things.

I just returned from two weeks in Greece for the second time in two years. Athens, Mykonos, then Santorini. Four nights in Santorini is perfect but to fly home, we went back to Athens for one night then took an early flight from ATH to LHR to get to SEA. Don't risk flights from Santorini to ATH on the day you want to fly home. Too stressful and risky. Do NOT rent a car on Santorini. Yes, taxis are expensive but finding a place to park is difficult. We stayed in Oia both times and I recommend Canavas Oia Suites. Oia is quiet and the sunsets are amazing. Great restaurants too. In Athens, I recommend Electra Rhythm Hotel on Ermou street. It is central to everything and moderately priced. Enjoy Greece, the people are very friendly.

That's exactly what we did after our RS Greece tour a few years ago. We stayed in Oia and used the bus to get around the island. On a night we knew we were coming back late from Fira, our host arranged for a car to pick us up because we didn't want to rely on finding a taxi. We also used our host to arrange for rides to and from the airport. The transfers averaged avout $40 if I remember correctly. We did rent a car for one day so we can explore the island. We didn't want to deal with trying to find parking so we did it this way. We also decided to fly back to Athens the day before our flight in case of delays or cancellations. I must say we had no problems with all our inter island flights and ferries as we also went to Mykonos before Santorini. Thanks to advice on this forum, we stayed at Hotel Avra in Rafina who offers free airport transfer shuttles. We loved our last night in the small port town of Rafina. We had dinner in the town square and watched all the locals come out for their dinners. Saw lots of families with their little kids come out and play in the square, too.