In a mixing bowl, beat the cream cheeses, sugar and vanilla until smooth. Fold in whipped topping. Arrange ladyfingers on the bottom and around the edge of an ungreased 9-inch springform pan.
Spread bottom layer with half of cream cheese mixture. Top with remaining ladyfingers (ladyfingers may overlap); spread with remaining filling. Cover and chill.
In a small saucepan, combine sugar and cornstarch. Stir in pineapple. Bring to boil over medium heat, stirring constantly. Cook and stir for 1-2 minutes or until thickened. Cool to room temperature; gently spread over torte. Cover and refrigerate for at least 4 hours or until set. Remove sides of pan.