Bring orange juice, sugar and rum to boil in heavy large saucepan, stirring to dissolve sugar. Stir cornstarch and 2 tablespoons water in small bowl to dissolve. Add cornstarch mixture to orange juice mixture; boil until thickened slightly, stirring constantly, about 1 minute. Add berries. Reduce heat to medium and stir until berries soften and are heated through, about 3 minutes. (Can be made 4 hours ahead. Let stand at room temp. Rewarm slightly before serving.)

Preheat oven to 250°. Whisk first 4 ingredients in large bowl to blend, then whisk in orange juice. Transfer to 15x10x2-inch glass baking dish. Add bread slices to egg mixture; turn to coat. Let stand until bread absorbs most of egg mixture, at least 5 minutes and up to 15 minutes, turning bread occasionally.

Heat griddle or 2 heavy large skillets over medium heat. Brush griddle with melted butter. Working in batches, cook French toast until browned and cooked through (firm to touch in center), about 3 minutes per side. Place on rimmed baking sheet and transfer to oven to keep warm.

Divide French toast among plates. Spoon berry compote over and dust with powdered sugar.