Heat oven to 350F
Combine the coconut flour, dried shredded coconut, baking powder, salt, 85 g butter, 100 g sugar, and egg white. Mix until combined, adding a bit of water if needed. Press into a greased tart pan, making the sides thicker than the bottom. Bake about 20 minutes, until golden brown and cooked through (you will not be baking it again after this). Set aside
Bring 12 oz cranberries, 1 cup granulated sugar, and 1/4 cup water to a boil in a large saucepan set over medium-high heat. Reduce heat and simmer until the cranberries burst and most of the liquid evaporates, about 15 minutes. Let cool and puree in a blender or food processor until very smooth
Cook puree, eggs, egg yolks, lemon zest, lime juice, salt, 1/2 cup sugar, and 1 tsp lime zest in a saucepan over medium-low heat, stirring constantly. Cook until it is very thick and coats spatula.
Using an electric mixer, beat in 1.5 sticks of butter one piece at a time, incorporating after each addition until curd looks lighter in color and texture, about 5 minutes. Scrape into crust and chill until firm, about 2 hours
Bring 1/2 cup granulated sugar and 1/2 cup water to a simmer in a small saucepan over medium heat, stirring to dissolve sugar. Add 4 oz cranberries and cook until barely starting to soften, about 1 minute. Using a slotted spoon, transfer cranberries to a wire rack set inside a baking sheet. Chill until no longer sticky, 20-30 minutes
Toss remaining 1/2 cup granulated sugar and 1 tsp lime zest in a small bowl. Toss cranberries in lime sugar. Top pie with cranberries and serve with whipped cream