Line the inside of the crust with aluminum foil and a layer of pie weights or dried beans.
Bake on the middle rack of the preheated oven until edge of crust is golden, 12 to 15 minutes.
Combine pumpkin, 2/3 cup sugar, orange juice, cinnamon, 1/2 teaspoon salt, and nutmeg in a bowl. Place egg yolks in a small bowl.
Place marshmallows in a bowl of boiling water. Stir well until melted. Add pumpkin mixture; stir until heated through.
Spoon about 1/4 of the pumpkin-marshmallow mixture into the bowl of egg yolks; stir back into the original mixture. Cover the bowl with plastic wrap and freeze until firm, at least 30 minutes.
Beat nondairy topping with an electric mixer until soft peaks form. Fold into the chilled pumpkin mixture. Pour into the pie crust. Cover with plastic wrap and freeze pie until set, 8 hours to overnight.
Preheat oven to 500 degrees F (260 degrees C).
Beat egg whites and 1/4 teaspoon salt in a bowl with clean beaters until soft peaks form. Add 1/2 cup sugar, 1 tablespoon at time, beating well after each addition until meringue is stiff and glossy. Fold in vanilla extract with a spatula. Spread meringue over the frozen pie.
Bake in the preheated oven until meringue peaks are golden, 1 to 2 minutes.