Combine pomegranate juice, orange juice, rum, 1/2 cup white sugar, brown sugar, cinnamon sticks, and cloves in a large pot; simmer until sugar is completely dissolved, about 10 minutes.
Peel pears, leaving stem intact. Slice 1/4 inch off the bottom for pears to stand securely.
Place pears gently in the pot and cover. Simmer for 30 minutes, basting pears every 5 to 10 minutes. Remove pot from heat and let stand for 30 minutes, continuing to baste occasionally. Remove pears from pot and set aside.
Strain spices from poaching liquid and add 1/3 cup sugar. Return to a low boil and reduce until sauce is thickened, 10 to 15 minutes.