Bring 12 oz. cranberries, 1 cup granulated sugar, and ¼ cup water to a boil in a large saucepan over medium-high heat.
Reduce heat and simmer until cranberries are bursting and most of the liquid has evaporated, about 12–15 minutes.
Let mixture cool and then purée in a blender until very smooth.
Please purée in a heatproof bowl set over a saucepan of simmering water (or in a double boiler) and add whole eggs, egg yolks, lemon zest, lime juice, salt, ½ cup sugar, and 1 tsp. lime zest.
Stir mixture with a rubber spatula scraping down sides of bowl when necessary, until curd thickens and coats spatula, about 8–10 minutes. Let cool until just warm.
Place curd in the large bowl of a stand mixer or in a large bowl if using a hand mixer. Beat on medium-high, while adding butter a piece at a time, incorporating after each addition. This will take about 5 minutes and curd will begin to look lighter in color and texture.
Pour the curd into the prepared crust and chill until firm, about 2 hours.
Bring ½ cup granulated sugar and ½ cup water to a simmer in a small saucepan over medium heat, stirring to dissolve sugar. Add remaining 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 rimmed baking sheet. Let rest for about 20-30 minutes, until cranberries are no longer sticky.
Toss remaining ½ cup granulated sugar and 1 tsp. lime zest in a small bowl. Add cranberries to lime sugar and toss until well-coated.
Top pie with cranberries and additional lime sugar, if desired.