Paros Recommendations?

You're missing the archaeological sites on Santorini, Akrotiri an Ancient Thera. Both are worth your time, especially Akrotiri. Do a google images search to see what they are. Go in the morning when they first open at 8am to beat the crowds from the cruise ship bus tours.

Not sure of your sequence but regular travelers to Greece recommend you do that Athens day at the end of the trip so you are in Athens the day before your return flight.

Its been a long time since we ate in Paros so I don't remember the tavernas but I have a method of choosing a taverna. The summer peak crowds will be greatly diminished by September so all the tavernas will not be full. We do a walk by, sometimes check the menu of a few tavernas but one thing is constant, there will be a few tavernas full of people while right next door they are virtually empty. The ones that are full will have a combination of great food and lower prices. Thats the one you should pick.

I haven't been to Santorini but if I did it would mainly be for the archeological sites, not so much the crowds and higher costs.

As far as eating in Paros or anywhere in Greece I would look for menus in Greek, not a lot of pictures of food or tavernas that look like more Greeks than tourists are there.

September will be the start of the off season so smaller islands like Paros will start to close down. However there will always be shops, markets and tavernas for locals which in the end may be a good thing because you'll be mingling with locals and going where they go. I'm sure they knew better where to eat than tourists who sometimes throw up their hands in the air because of so many tavernas to pick from.