Heat soymilk in a sauce pan with the cornstarch whisked in. heat until gently simmering and slightly thickened. Add sweetener and remove from the heat. Stir until combined and sweetener dissolves.
Puree all of the fruit and juice together and add to the soymilk. Combine thoroughly and chill in the fridge for 2-3 hours.
Freeze in your ice cream maker according to the models instructions!
You could try to freeze the batter 3/4 of the way, smooth in a food processor, and freeze again.....