Bring the rice, water, and salt to a boil in a pot; cover, reduce heat to medium-low, and simmer until the rice is tender and the liquid has been absorbed, 45 to 50 minutes.
Stir the evaporated milk, maple syrup, cinnamon, nutmeg, vanilla extract, and rum extract into the cooked rice. Continue simmering until the mixture thickens, about 5 minutes.