Stud each orange with 6 whole cloves, using the pointed ends of the cloves to pierce the skin. Cut oranges into wedges. Reserve 12 wedges for garnish. Cut some slits into each hawthorn.
Bring water, hibiscus petals, and cinnamon sticks to a boil over medium-high heat. Reduce heat and simmer until water is a deep pink color, 10 to 15 minutes.
Remove hibiscus petals but leave cinnamon sticks in the water to infuse further. Stir in orange wedges, hawthorns, apples, sugar cane, pear, and brown sugar. Simmer, stirring occasionally, for at least 30 minutes.
Ladle the punch into 12 mugs, making sure each mug gets some slices of fruit. Add 1 fluid ounce rum to each mug to give the punch an extra kick. Garnish mugs with reserved orange slices.