Slice bread into 1/2-inch-thick slices and remove crusts. Ladle about 1/2 cup cooked berry mixture into bottom of soufflé dish (approximately 7 1/2 inches across by 3 inches high). Arrange one layer of bread slices side by side in a circular pattern (this will become the top when pudding is unmolded); add more berry mixture to saturate. Continue adding bread, slicing to fit mold, and berry mixture. Finish with bread, and top with any remaining berry mixture.
Cover pudding loosely with plastic wrap and place a plate (with approximately the same diameter as inside of mold) on top. Weight with a heavy can and refrigerate. Remove weight after 6 to 8 hours. Continue to refrigerate overnight or up to 2 days.
To make topping:
In a small bowl, whip cream until it starts to thicken. Add sugar, vanilla and rum. Continue to whip until stiff peaks form.
Run a knife around outside of pudding; unmold upside down onto a serving plate. Garnish with fresh fruit. Serve in wedges with whipped cream.