Crust: 1. Heat the oven to 350 degrees. Use cooking spray to coat an 8-inch round tart pan with a removable bottom.
In a food processor, combine the flour, almonds, sugar and salt. Process until the almonds are finely ground. With the processor running, add the butter one piece at a time. Add the cream cheese by the tablespoonful, pulsing twice after each addition, until incorporated.
Turn the dough out into the prepared pan (it will be crumbly). Spread the dough evenly and press firmly into the bottom and up the sides of the pan. Bake until lightly browned, 20 to 25 minutes. Let cool on a wire rack.
Filling: 1. In a small saucepan over medium-high, whisk together the lime zest, lime juice, water and half the sugar. Heat until simmering.
In a medium bowl, whisk together the remaining sugar, egg yolks, cornstarch and salt. While whisking, pour a small amount of the hot lime water into the yolks to warm the mixture, then continue to add more until all the lime water is incorporated. Pour the mixture back into the saucepan and cook over medium-high, whisking continuously, until the mixture is thick, about 2 to 3 minutes. Remove the pan from the heat and whisk in the butter until fully incorporated.
Pour the filling into the cooled tart shell, spreading it in an even layer. Press a piece of plastic wrap over the surface of the filling to prevent a skin from forming. Refrigerate until the filling is well chilled, about 1 hour.
Cut the melon into quarters, then trim the rind from each section and cut the flesh into thin symmetrical slices. Arrange the slices overlapping around the outside of the tart shell, with the narrow ends pointing in. Mound the berries in the center of the tart. Refrigerate until ready to serve.