The 1730 Blue Star arrives on Paros at 2230, then arrives on Naxos about an hour later. Since you are arriving in Athens on a Friday, it's possible there will also be a Hellenic Seaways highspeed leaving that afternoon and arriving on Paros much earlier. Last year on the corresponding Friday (June 1st) Highspeed 4 departed Piraeus at 1600 and arrived on Paros at 1835. With a 1250 arrival in Athens you will have plenty of time to get to Piraeus by bus or taxi. The X96 bus goes directly to the port, and takes about 1hr 15min.

You will have to wait until spring for the Hellenic Seaways timetables to be released, and this particular ferry company changes its schedule year-to-year. Neither Blue Star nor the highspeed are likely to be fully booked, so it is safe to wait until April or early May to reserve seats on the ferry. In fact, I always wait until arriving in Greece to buy my ferry tickets. In the meantime you can keep checking the Olympic Air website to see if they offer a later flight. In my experience they sometimes make changes to the summer schedule, and in the past have had a flight around 1800-1900.

I agree re: no need to buy tickets ahead of time. Late May/early June you can buy the tickets at the port.