Combine first 11 ingredients in a large mixing bowl. Cover and refrigerate until ready to serve.
Shuck each oyster by carefully inserting the point of an oyster knife at the hinge end of the shells and twisting. (Don't lose the juices.) Discard top shells. Free the oyster from the bottom shell by gently sliding a knife underneath it. Serve with Pickled-ginger Salsa.
Chef John Recommends: A citrusy, non-oaked Sauvignon Blanc. Alternative Pour: A lean California brut sparkling wine.