Beat first 5 ingredients at high speed with an electric mixer 45 seconds or just until blended. Gently fold in whipped cream. Divide mixture into 2 portions. Fold melted chocolate into 1 portion. Set both mixtures aside.
Stir together coffee and rum.
Split ladyfingers in half. Arrange enough ladyfingers to cover bottom of a 3-quart trifle dish or other glass bowl. Soak ladyfingers with coffee mixture. Top with half of chocolate cheese mixture. Add another layer of ladyfingers; soak with coffee mixture. Top with half of cream cheese mixture. Repeat layers with remaining ladyfingers, coffee and cheese mixtures, ending with cream cheese mixture. Cover and chill trifle 8 to 24 hours. Grate white chocolate using a vegetable peeler, and pile shavings in center of trifle just before serving.
*As a substitute for mascarpone cheese, combine 2 (8-ounce) packages cream cheese, 1/3 cup sour cream, and 1/4 cup whipping cream; beat well. Use 2 cups for recipe, reserving remainder for other uses.