In a large bowl, combine the mascarpone cheese, cream cheese, and vanilla extract. Using an electric hand mixer or stand mixer, whip on high speed until smooth and well blended. Add the powdered sugar and continue whipping on high speed until fully incorporated. Using a rubber spatula, gently fold in the whipped cream until the mixture is light, fluffy, and evenly combined. Stir the rum or rum extract into the coffee, then dip the ladyfingers one by one into the coffee mixture. Arrange a layer of soaked ladyfingers evenly across the bottom of a 9x13-inch pan. Spread half of the mascarpone mixture over the ladyfinger layer, smoothing it out, and dust the top with cocoa powder. Add another layer of coffee-soaked ladyfingers over the cocoa-dusted mascarpone, then top with the remaining mascarpone mixture, smoothing the surface as much as possible. Cover the pan with plastic wrap and refrigerate for at least 2 hours or overnight. Just before slicing and serving, dust the top with the remaining cocoa powder.