Combine the rum, raisins, dried cherries, and dried cranberries in a bowl. Heat in the microwave for 1 minute and let sit for at least 10 minutes. Drain the rum and set aside.
Combine the almond milk and yeast in a large bowl. Let it rest for 5 minutes, allowing the yeast to become active. Combine the flour, salt, cinnamon, cardamom, allspice, nutmeg, ginger, orange zest, and lemon zest.
Place the butter in a large bowl and mix until whipped. Add the sugar and mix until combined. Add the eggs and almond extract.
Add a third of the flour mixture and mix. Add another third, mix, and then the final third.
Add the dried fruits and knead into the dough. Lightly flour a countertop and knead the dough for five minutes. Smooth the dough into a ball. Spray a large bowl with nonstick spray. Place the dough ball into the bowl and cover the bowl with plastic wrap. Allow to rise until it doubles in size, about 1 to 2 hours.
Divide the dough into 14 - 16 equal portions. Shape into round balls and place on the baking sheet. Cover with plastic wrap and let rest for 30 to 60 minutes, or until doubled in size.
Preheat an oven to 350°F. In a small bowl, whisk the ingredients for the spirals until smooth. You want the mixture to be thick but thin enough to pipe. Transfer to a ziplock bag. Cut a small hole in one of the corners.
Make spirals on top of each of the buns. Place in the oven and bake for 20 to 25 minutes or until golden brown.
To make the glaze, combine the orange juice, water, and sugar in a saucepan over medium-high heat. Bring to a simmer. Simmer for 3 to 5 minutes until slightly thicken. Brush each of the buns with the glaze.