Combine sweetened condensed milk, coconut milk, milk, egg yolks, and cornstarch in a saucepan over low heat; cook, stirring constantly, until thickened into a custard, about 10 minutes.
Divide custard between 2 bowls. Mix 2 2/3 cups shredded coconut into the first bowl of custard. Fold cocoa powder into the second bowl of custard. Let custard mixtures cool, about 10 minutes.
Beat cream in a chilled glass or metal bowl with an electric mixer until soft peaks form.
Pour 1/4 cup milk into a shallow bowl. Dip ladyfingers briefly in milk and arrange in the bottom of a glass trifle bowl. Spoon coconut custard on top. Layer remaining ladyfingers and chocolate custard on top. Smooth whipped cream over the top.
Place 1 1/3 cup shredded coconut in a small skillet over low heat. Cook and stir until toasted and fragrant, 3 to 5 minutes. Sprinkle toasted coconut over whipped cream.
Shave chocolate into long curls with a vegetable peeler; scatter over coconut.
Cover trifle with plastic wrap and refrigerate until flavors meld, about 4 hours.