In a large bowl, stir together nutmeg, ginger, raisins, dates, nuts, sugar, and flour.
In another bowl, mix baking soda with 3 tablespoons hot water. Add persimmon pulp and whisk to mix well. At once add eggs, 1/3 cup rum, vanilla, and butter and whisk to blend.
Add persimmon mixture (it thickens) to dry ingredients and stir until batter is thoroughly moistened.
Scrape batter into a buttered 9- to 10-cup pudding mold with a tube; cover tightly. Elevate a rack at least 1 inch in a pan deep enough to hold pudding mold (8 qt. or larger). Pour water up to top of rack. Set pudding on rack. Cover pan and bring water to boiling. Keep water at a rapid boil, adding more hot water as needed to maintain water level.
Steam pudding until it feels firm when pressed lightly in the center, about 2 1/2 hours.
Uncover pudding and let stand until slightly cooled, 20 to 30 minutes. Invert onto a dish and lift off mold. Serve. Or let the pudding cool, then return to mold and cover, or seal in foil, and chill up to 4 days. To reheat, steam pudding in mold (or sealed in foil) on rack above simmering water until hot, at least 45 minutes.
To flame, warm remaining rum in a 2- to 4-cup pan until bubbling at edges. Carefully ignite with a match (not beneath or near a fan, vent, or flammables) and pour slowly over pudding. Slice and serve.