The day before: chop dates into small pieces and put in a glass bowl. Add rum. Cover with plastic wrap. Let sit for 8 hours, or overnight, to absorb the rum. You can leave this step out if you want but I find it makes the dates more delicious and the cookies have more flavor.
Preheat the oven to 375 degrees F (190 degrees C). Line baking sheets with parchment paper.
Dice candied cherries and pineapple into small pieces and place in a very large bowl; I use the top of my cake carrier. Add pecans, followed by dates. Add 1 cup flour. Toss well to coat all of the pieces and break them up so they are not sticking together.
Whisk baking soda into the milk and let it dissolve.
Mix shortening into the fruit. Add remaining flour, sugar, eggs, orange juice, nutmeg, salt, and milk-baking soda mixture. Mix together with your hands just until you no longer see the flour. Try not to overmix. The batter will be very dense.
Use a small ice cream scoop or two teaspoons to drop the cookies onto the prepared pans, about 1 inch apart.
Bake in the preheated oven until golden brown, 10 to 12 minutes. Cool on wire cooling racks.