Arriving in Athens very early morning before RS Tour.

We have stayed at Peris hotel. Its fairly nice and includes a breakfast. They offer a free shuttle service to and from the airport but do charge a fee if you need the shuttle between midnight and 6 AM. You are probably looking at maybe 120 euros. The shuttle trip is about 15 to 20 minutes. Frankly the time saved by just walking across the street and into Sofital is probably worth the extra few dollars (euros) for a 1:30 AM arrival.

The Sofitel is expensive, yes, but the time you save by booking there will allow you at least an extra hour's sleep. Keep in mind that you'll be taking a taxi to any other hotel that's close to the airport and taxi prices are higher after midnight, so factor that into the overall expense of staying somewhere other than the Sofitel. I think the only hotel available at that late hour that's closest to the airport would be the Athens Holiday Inn. I don't know if it's still offered but they used to have a free airport shuttle service. You don't say when your RS Tour is scheduled to depart or from where, but that also needs to be factored in to your decision as to where to stay. There is an airport express bus (X95--every 20-30 minutes) that takes 45 minutes to reach central Athens for only €6pp. It ends alongside Syntagma Square and close by just a block down Mitropoleos Street is the Arethusa Hotel, which is quite reasonably-priced. Look at this map to see it's only 180 meters' walk: https://tinyurl.com/yakbpwkb

Peri's Hotel, St. Thomas B&B and Pantheon Hotels are all close to the airport but the question is whether or not you can check in so late. They all have websites.

I have to agree with the Sofitel for convenience & your arrival time. We chose Sofitel (2017) the night before our departure. Our last destination was Santorini. We had booked the hotel months in advance and were fortunate to snag a lovely room, comfortable bed, excellent breakfast (extra) for a about $170. The ease of walking across from the terminal directly into the hotel was worth the expense. BTW the RS Greece tour was one of our favorites! Enjoy.

Is it too late to book a different flight?

A few hours sleep could be worth the $200 in your situation.

Take a taxi (about 30 minute drive - no traffic then) to the tour hotel. That way you don't have to repack and possibly (probably) not have access to your room in Athens until mid-afternoon. You can sleep late or go to breakfast and have a walk around and then go back to rest for a few hours before the group meeting.