In a saucepan over medium heat, carefully bring rum and dried fruit (apricots, cherries, raisins and cranberries) to a boil; if the rum ignites, simply allow the alcohol flame to die out. Reduce until rum is nearly gone, approx. 3 min; immediately add kombucha, orange juice, brown sugar, cinnamon sticks and apricot preserves and return to a low boil, then remove from heat.
Preheat oven to 325 degrees. Remove all packaging from ham, including bone cap. Make several slices across top of ham about 1” apart and 1/4” deep in a diamond pattern to allow glaze to penetrate meat. Transfer ham to roasting pan and completely cover the top with citrus slices; if some fall off, leave in pan until end steps. Pour glaze and fruit over and around ham and cover tightly with lid or parchment and foil.
Bake until internal temp reaches 120 degrees in deepest part of meat (approx. 1.5 hours). Remove cover and increase heat to 375 degrees. Baste with pan juices and spoon fruits over the top of the ham; the fruit should be sticky enough to stay in place as the glaze sets. Continue cooking approx. 30 min until deepest part of ham reaches 135 degrees, basting every 5 min with pan juices to create a shiny, finished glaze.
Remove from oven and let rest 10 min until internal temp reaches 140 degrees. Carefully transfer ham topped with fruit to serving platter, reserving juices. Pour juices into a saucepan over high heat and reduce until slightly syrupy, approx. 3 min; pour over ham and fruit and serve immediately.