In a medium-size saucepan, combine 3 cups of the berries with the water. Bring to a boil. Let cool, then strain to remove the seeds. Return the syrup to the saucepan. Stir in the cornstarch, sugar, and lemon juice. Bring to a boil, stirring, and boil for 2 minutes. Cool.
When the syrup is cool, blend the cream cheese, milk, and lemon zest until smooth. Spread evenly in the baked pie shell. Top with the remaining 2 cups uncooked berries. Pour the cooled, thickened syrup evenly over the berries. Refrigerate for 1 hour or more.
Just before serving, decorate with whipped cream and/or additional fresh berries.