I recognize you don't like to fly so the ferry may be appealing. However you will have just flown for at least two flights and about 14 to 18 hours. If you wait 2 more hours you can take the next 45 minute connecting flight to Santorini on a modern jet and be in your hotel relaxing and viewing the caldera. Get over jet lag on an island.
Athens is foreign, it is dusty, hot, confusing and somewhat chaotic. With experience we never stop in Athens at the beginning of a holiday. We always keep Athens to the end. by that time we are in the swing of the Greek tempo and Athens is much easier to experience.
While taking the ferry sounds romantic it is going to eat up virtually a full day of your three in Santorini. I don't think that is a good use of time and resources. If you take a fast ferry it will probably cost almost as much as the flight. Check Aegean airline web site.
You will have to ferry from Santorini to Naxos. Thats about a 2.5 hour trip. That is enough ferry cruise around the islands for me.
August is absolute high season. You should be looking for hotels now. You may find your choices are getting more expensive every day as supply dries up.
I have never seen a sofa bed in our Greek travels. Many hotels have three single beds. If it were me I would be looking for two separate rooms. On Naxos there are lots of very nice very simple studio hotels right on the beach with ocean views and reasonable prices. Check out Sigma Studios, Diogenes Studios, Hotel Spiros, Studios Naxos Thomais studios and Hotel Kymata. All are on St George beach all have direct ocean view. They are all small. They are a a place to sleep and sit on the balcony and have a wine and enjoy the view. In a totally different class and probably already sold out is Boutique Hotel Glaros.
I am suggesting you stay at St George beach. It is part of Naxos town so you get a beach holiday with all the benefits of town being a 10 minute waterfront stroll into the main waterfront Promenade.
Go to booking dot com and punch in your destination and dates. It will give you availability rates and reviews. Search for Agios Georgeos.
Naxos Town http://www.flickr.com/photos/stanbr54/sets/72157632094558042/
Trip around Naxos http://www.flickr.com/photos/stanbr54/sets/72157634605629689/
St George Beach Hotels Naxos http://www.flickr.com/photos/stanbr54/sets/72157632162394787/
St George Beach Naxos http://www.flickr.com/photos/stanbr54/sets/72157632113170279/
Another option would be Studio Glaros. It is in a residential neighborhood but is only a 3 minute walk to the beach. It has multi bed units. We have stayed there several times but their web site shows it has been totally remodeled since our last stay. All of these hotels are in the album above.
For your beach days where you just want to spend the day on the beach there are better beaches than St George. We head out about 7km to the west coast beaches generally Plaka beach. A car makes this an easy day but public bus is every half hour and very inexpensive.
Plaka beach tavernas hotels https://www.flickr.com/photos/stanbr54/sets/72157655106193251