As you state, we are now in "prime beach season" for New England as the greenheads and other biting flies are mostly gone. Also, the water temps rise all through September even while the air temperature cools substantially. My favorite time for the beaches is mid-September. Not sure I'm going to be able to work a trip in this year though.
What is great about Plum Island is that the southern half of the island has parking lots one mile apart. There are only 20 parking spots at these. The very southern tip is a MA state park. It only has 55 parking spots.
So, if you get there early enough in the off season, you can literally have a 1/4 mile or more beach to yourself. Especially between lots 5 and 6.
It is Parker River National Wildlife refuge. There are a lot of bird watchers there. So, many people that go there do not really care about going to the beach. There are no bathrooms at these smaller parking lots except for the northern and southern tip of the island. No boogy boards, surf boards, paddle boards allowed either. People do clam out in the tidal flats.
In the early summer they literally close down miles of beach for the nesting Piping Plovers. They have “Plover Wardens” stationed on the beach to keep you from walking onto the closed sections. The state beach at the south end will fence off sections of the beach where Plovers are nesting, but not shut down 2 miles of beach.