Toss the mango and blueberries with rum and sugar in a medium bowl. Let the fruit macerate until soft and juices have accumulated in the bowl, 25–30 minutes. Stir occasionally.
In a medium bowl, use a hand mixer to whip the heavy cream and vanilla in a medium bowl until soft peaks form.
In six glasses, layer a crushed meringue cookie in the bottom of each glass. Top with 1/4 cup fruit and whipped cream on top. Add a second layer of crushed meringue, fruit and whipped cream.
Can be made 20-30 minutes ahead and chilled in the glasses. Or each component can be made up to a day ahead, with the fruit and whipped cream refrigerated and the meringues stored at room temperature.