Well, I love to go to Ag. Prokopios beach to swim, but not that fond of staying there. Truth is Ag Anna, Plaka & Ag. Prokopios are each really a strip of hotels built at the edge of former farm fields, flat, scrubby, bamboo stands. The hotel you have picked Ag. Pro. Hotel, is a biggie sort of hotel w. pool etc,lots & lots of concrete and if you look closely on the google map of booking.com, it's waaay back from the beach surrounded by ex-farm... to reach the sand, u have to walk downhill on the busy road ... The only place I like much in Ag. P is Liana Studios, because it's almost the only one directly on the beach -- its own website is malfunctioning but TA has some reviews & good traveler photos of the sort of views you get -- https://www.tripadvisor.com/Hotel_Review-g805487-d1195023-Reviews-Liana_Hotel-Agios_Prokopios_Naxos_Cyclades_South_Aegean.html
By contrast, Ag Giorgios is well-established, trees & shade, Greenery, no dusty-field feeling. As for a very special place, what I think would be perfect for you IF you can book it, is VILLA NAXIA. http://www.villa-naxia.gr They don't use booking.com or other agencies (they don't need to), you must contact them direct, but since your dates are October, you have a good chance. Just look at their photo gallery and you will see .... at the very far end of Ag. Giorgios, but direct access to beach, building off on its own VERY well-appointed, balconies & terraces w. sea view... frankly if I were on my anniversary trip that's where I'd go.
BTW, I love all the places on your list, but you DO seem to be hopping around a HUGE amount for just 14 days! Well, I'm sure you are well-organized, and you'll be "sampling" for your return visits. Comment on various places:
• SIFNOS - In Artemonas, I always eat at Margaritas (?) on the square, great mezedes.
• MILOS - hope u plan island-rim boat trip; if it's windy I recommend the big catamaran, and the half-round trip.