Preheat the oven to 375 degrees F. Slice off and reserve the top 1 1/2 inches of the pumpkin. Scoop out the seeds and stringy pulp.
Melt 2 tablespoons butter in a large skillet over medium heat. Add the bread and cook, stirring occasionally, until golden, about 4 minutes; transfer to a bowl. Add the remaining 1 tablespoon butter, the apples, brown sugar and raisins to the skillet and cook until the apples are crisp-tender, about 4 minutes. Stir in the rum, vanilla, cinnamon and a pinch of salt. Return the bread to the skillet.
Put the pumpkin in a small baking dish and fill the pumpkin with the apple mixture. Cover with the pumpkin top and add 1 inch of boiling water to the baking dish. Cover loosely with foil and bake until the pumpkin is tender, 2 hours to 2 hours, 30 minutes. Remove the foil and pumpkin top and return the stuffed pumpkin to the oven. Bake until the filling is lightly browned, about 10 more minutes. Transfer to a serving plate and drizzle with maple syrup. To serve, scrape the pumpkin flesh and stir into the apple mixture.