To prepare custard, combine first 6 ingredients in a medium saucepan, stirring with a whisk. Let stand 5 minutes. Bring to a boil over medium heat, stirring constantly. Cook for 30 seconds, stirring constantly. Remove from heat. Stir in 2 tablespoons rum and extracts, and pour the mixture into a large bowl. Cover and chill 2 hours.
To prepare the apricots, combine the preserves and remaining ingredients in a medium skillet; bring to a boil. Reduce heat, and simmer for 5 minutes or until the apricots are soft, stirring occasionally. Serve over custard.