The Madison Surf Club (so named, despite the lack of surf) has a fleet that stays on the beach all season long. You may be able to keep your boat there. I don't know what costs are involved or if you have to be a member of madison or not, but it might be worth checking out. I don't have any contact information, unfortunatly.
Also, I live in West Haven, and plan on having a 16 in the water by Summer, if all goes well with the boat I want to buy now, and I'd be happy to have another to sail with. I've got a couple friends with the boats too. And as you said, New Haven (five mins from me) is due south of you.
A ship in harbor is safe -- but that is not what ships are built for.