Place apricots and water to cover in a medium saucepan. Bring to a boil. Reduce heat; cover and simmer 30 minutes. Drain well.
Place apricots in container of an electric blender; process until smooth. Return apricot puree to saucepan. Stir in 3/4 cup sugar and 1/2 cup water. Bring to a boil, stirring until sugar dissolves. Remove from heat. Cool to room temperature. Chill thoroughly.
Combine remaining sugar and corn starch in a heavy saucepan, stirring well. Stir in cold milk. Gradually add scalded milk, stirring constantly.
Beat egg yolks until thick and lemon colored. Gradually stir one-fourth of hot milk mixture into egg yolks; add to remaining hot milk mixture, stirring constantly. Return to low heat; cook, stirring constantly, until smooth and thickened. Remove from heat. Cool to room temperature. Stir in flavorings.
Beat egg whites (at room temperature) until soft peaks form. Fold into custard mixture. Chill thoroughly.
Beat whipping cream until soft peaks form. Fold into custard mixture.
Line bottom and sides of a lightly greased glass 2-quart soufflé or serving dish with split ladyfingers. Spoon half of custard mixture into dish; top with a layer of ladyfingers. Spread apricot mixture over ladyfingers; top with another layer of ladyfingers. Spoon remaining custard mixture over ladyfingers. Top with remaining ladyfingers. Cover and refrigerate overnight.
Top with sweetened whipped cream; sprinkle with grated orange rind. Spoon into individual serving dishes to serve.