Preheat the oven to 350°F. Lightly grease (or line with parchment) two baking sheets., In a large mixing bowl, combine the butter, shortening, sugar, baking powder, baking soda, spices, salt, vanilla, and rum, beating until smooth., Add the eggs one at a time, beating well after each addition; then add the boiled cider or syrup., Stir in the fruit and nuts, then the flour and oats, beating gently until well combined., Drop balls of dough onto the prepared sheets, leaving about 2" between them; see "tips," below., Bake the cookies until they're just barely set on top: about 12 minutes for the small cookies, 13 to 14 minutes for the medium cookies, and 16 minutes for the large cookies., Remove the cookies from the oven, and cool them on the baking sheets, or transfer them to a rack to cool., Store cooled cookies at room temperature, well wrapped, for 3 to 4 days; freeze for longer storage.