Coat the bottom and sides of an 11-by-17-inch rimmed baking sheet with cooking spray. Prepare the cake mixes as directed; spread in the baking sheet, filling it about three-quarters of the way (you will have leftover batter).
Bake the cake at 350 degrees F until a toothpick comes out clean, 15 to 20 minutes. Let cool in the pan, then scrape off the top of the cake with a fork, leaving a border for the crust.
Cut the fruit leather into 1 1/2-inch circles using a cookie cutter or kitchen shears and set aside. (If the strips are too narrow, roll them out slightly with a rolling pin before cutting.)
Grate about 2 tablespoons of white chocolate into a bowl and set aside. Chop the remaining white chocolate.
Microwave the chopped white chocolate in a microwave-safe bowl in 30-second intervals, stirring, until smooth.
Mix the preserves with 2 tablespoons of the melted white chocolate in another bowl ¿ this will make the sauce more opaque.
Spread the strawberry sauce on the cake, inside the border.
Top with spoonfuls of the remaining melted white chocolate, spreading each slightly with the back of a spoon. Sprinkle with the grated white chocolate.
Use a kitchen torch to toast the melted white chocolate and the edges of the cake. Top with the fruit-leather circles.