Make the meringue: Pulse flours and confectioners' sugar in a food processor until combined. Sift 3 times.
Preheat oven to 275 degrees. Line 2 rimmed baking sheets with parchment, and draw two 7-inch circles on each. Flip parchment over. Whisk whites, cream of tartar, and superfine sugar with a mixer on medium speed until combined. Gradually increase speed to high, and whisk until stiff peaks form, about 10 minutes. Add vanilla. Fold in flour mixture in 3 batches, adding each batch before previous batch is fully incorporated. Spoon batter into a pastry bag fitted with a 1/2-inch plain round tip. Starting in center of each circle, pipe a tight spiral to edges. Bake until dry and crisp but not browned, 45 to 50 minutes. Let cool on sheets.
Make the pineapple: Puree 1/2 cup fresh pineapple, and reserve for buttercream. Mix juice, granulated sugar, and salt in a large skillet over medium heat. Cook, whisking occasionally, until sugar dissolves. Add the remaining pineapple slices to skillet. Bring to a simmer, and cook until pineapple is light golden brown and liquid is syrupy, 45 minutes to 1 hour. (Add more pineapple juice if liquid evaporates too quickly.) Let cool in skillet.
With a slotted spoon, remove pineapple slices from syrup, and coarsely chop. Puree 1/2 cup caramelized pineapple with 2 tablespoons syrup, and reserve for buttercream. Transfer remaining caramelized pineapple to a bowl and syrup to another bowl.
Make the pineapple buttercream: Bring sugar, corn syrup, and water to a boil in a small saucepan, stirring until sugar dissolves. Wash sides of pan with a wet pastry brush to prevent sugar crystals from forming. Boil, undisturbed, until mixture registers 245 degrees on a candy thermometer.
Meanwhile, whisk yolks with a mixer on high speed until pale and thick, about 5 minutes. Reduce speed to low, then pour hot syrup in a slow, steady stream down side of bowl. Increase speed to high, and whisk until mixture is pale, thick, and warm, about 5 minutes. Reduce speed to low. Add butter, 1 tablespoon at a time, mixing after each addition. Increase speed to high, and whisk until smooth.
Reduce speed to low, then add caramelized pineapple and fresh pineapple purees. (Buttercream will keep, covered and refrigerated, for up to 3 days. Bring to room temperature, then beat on low speed before using.)
Make the praline: Line a baking sheet with parchment, then coat with spray. Bring sugar and pineapple juice to a boil in a small saucepan over medium-high heat, stirring until sugar dissolves. Wash sides of pan with a wet pastry brush to prevent sugar crystals from forming. Cook, undisturbed, until mixture turns amber and registers 320 degrees on a candy thermometer.
Remove pan from heat, wait until bubbles subside, then stir in almonds. Immediately pour mixture onto prepared parchment. Using an oiled offset spatula, spread to a 1/4-inch thickness. Let cool, then finely chop.
Assemble the cake: Place 1 meringue layer on a platter. Gently brush layer with 2 tablespoons reserved caramelized pineapple syrup. Spread 1/3 cup chopped caramelized pineapple on top. Spread 3/4 cup buttercream on top, then sprinkle with 3 tablespoons chopped praline. Repeat twice, then top with remaining meringue circle. Refrigerate until buttercream is firm, about 1 hour. Cake will keep, uncovered and refrigerated, for up to 1 day. Garnish with more praline if desired.