Preheat the oven to 375°F and set an oven rack in the middle position. Line an 8-inch baking dish with heavy-duty aluminum foil (so that there is an overhang on at least 2 sides) and spray lightly with nonstick cooking spray.
Make the crust: In a medium bowl, combine the graham cracker crumbs, melted butter, brown sugar, and salt. Stir until well combined, using your fingertips if necessary to be sure no lumps of brown sugar remain. Press into the bottom and 1 inch up the sides of the prepared pan. Bake the crust for 10 minutes, until set. Remove the crust from the oven and set aside. Reduce the oven temperature to 325°F.
Make the batter: In the bowl of an electric mixer fitted with beaters or the paddle attachment, beat the cream cheese, granulated sugar, and flour together on medium speed until just smooth, about 1 minute. Add the sour cream, eggs, vanilla, lemon zest, lemon juice, and salt; beat on low speed until just combined, about 1 minute. Do not over-mix.
Pour the batter into the slightly cooled crust.
Smooth out batter and drop the strawberry preserves by half teaspoons over the top of batter. Use a toothpick and swirl the preserves. Drop the 1/2 cup of blueberries over the top. Check to make sure your oven has cooled to 325°F, then bake for 45 to 55 minutes, until the filling is set but still a little jiggly in the center. (An instant-read thermometer, inserted into the filling about 1" in from the edge, should read between 180°-190°F.) The cheesecake will continue to cook as it cools. Remove from the oven, and cool at room temperature for 30 minutes. Refrigerate until cold, at least 6 hours but preferably overnight.
Use the foil overhang to lift the cheesecake out of the pan and onto a cutting board. Cut into squares, wiping the knife clean with a damp cloth between slices. Refrigerate until ready to serve.