Spray the inside of a 9-inch springform pan that is at least 2 1/2 inches tall evenly with nonstick cooking spray. Set aside.
Process the chocolate wafer cookies, 2 tablespoons granulated sugar and 1/4 teaspoon salt in a food processor until the cookies are broken down into fine crumbs. Add the melted butter and pulse until just combined and the mixture resembles wet sand. (Do not overmix or the crust will become pasty.) Press the crumb mixture into the bottom of the prepared pan, then freeze while you make the cheesecake mixture.
Combine 1 package gelatin with 2 tablespoons water in a small microwave-safe bowl and set aside to soften, about 5 minutes.
Beat the cream cheese in a large bowl with an electric mixer on medium-high speed until completely smooth, about 1 minute. Scrape down the sides of the bowl. Add the confectioners' sugar, sour cream, lemon juice, vanilla and a pinch of salt and beat on medium-high speed until incorporated and smooth, about 1 minute.
Microwave the gelatin and water, stirring as needed, until melted, about 30 seconds. Add the gelatin to the cream cheese mixture and beat on medium-high speed to combine, about 30 seconds.
Pour the cream cheese mixture into the springform pan and smooth out the top. Tap the pan a few times on a tabletop to release any air bubbles in the cheesecake. Cover with plastic wrap and refrigerate until set, about 2 hours.
Once the cheesecake is set, prepare the white wine gelatin. Pour the white cranberry juice into a medium saucepan and sprinkle over the remaining 3 packages gelatin. Let sit until the gelatin is absorbed, 2 to 3 minutes.
Add the remaining 1/4 cup granulated sugar and heat over low heat, whisking occasionally, just until the gelatin and sugar dissolve, 1 to 2 minutes. Pour the gelatin mixture into a large liquid measuring cup and stir in the white wine. Use a spoon to scoop away any bubbles at the surface. Refrigerate, stirring every 10 minutes, until the gelatin just begins to thicken and is the consistency of thin fruit jelly, 30 to 45 minutes.
Meanwhile, gently push a blueberry into the cavity of each lychee. Press the eyeballs firmly into the cheesecake layer, creating a spiral design. Dip a toothpick into the red food coloring and paint lines on the lychees to resemble bloodshot eyeballs.
Gently pour the wine mixture evenly around the fruit, coming up about 1/4 inch. Refrigerate until set, about 10 minutes. Pour the remaining gelatin mixture over the cheesecake and refrigerate until completely set, at least 4 hours and up to overnight.
Use an offset spatula to carefully loosen the sides of the cheesecake from the pan, then open the clasp and remove the outer ring. Cut into slices and serve immediately.
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