In a small bowl, place apple juice and 2 tablespoons water. Sprinkle gelatin powder over liquid; set aside to soften, about 10 minutes.
Beat eggs in an electric mixer at medium-low speed until fluffy.
Combine the rest of the sugar (3/4 cups) and 1/4 cup water in a small saucepan over medium-high heat.
Cook, stirring occasionally about 5 minutes until the sugar water turns into a firm ball.
With the mixer at high speed, drizzle sugar mixture into eggs. Beat about 5 minutes, until mixture turns pale yellow.
Place bowl with softened gelatin over a saucepan of simmering water and stir until gelatin dissolves.
Turn mixer to low and add gelatin to egg mixture.
Add pumpkin purée, 1/2 teaspoon cinnamon, 1/4 teaspoon nutmeg, allspice, ginger, salt, and sour cream and combine.
Pour filling into pie crust and refrigerate until set, at least four hours.