You can get through the channel to Watch Hill. Just make sure you stay in the channel or you will surely go aground. Watch Hill is one of my favorite places. Great beaches, good convenient anchoring area, and charming town.
Chances are getting a mooring in the Great Salt Pond during peak season is slim. They are first come first served. One way is anchor the first night and then circle the mooring area the following morning to scout out who's leaving and grab it immediately.
I would avoid Mattituck. Long narrow channel and shoaling is always an issue. Better choices for stopping along the CT shore.
Best harbor on Fishers Island is West Harbor. They make you anchor outside the mooring area but the protection is decent and holding is good.