Rinse and drain the rice and place in bowl. Cover with water and stir in 1 T salt. Let soak for 2 hours, then drain.
Boil 6¼ c water, add the rice and remaining salt, and stir well. Boil for 5 minutes, uncovered, then drain again. Set aside.
Combine saffron and sugar, then stir in 1 t warm water and all but 2 T of oil.
Transfer this mixture into the saucepan and add the potatoes, stirring and flipping until well coated.
Arrange the potatoes on the bottom of the pan, top with rice, and drizzle with remaining oil. Cover and cook over medium heat for 5 minutes.
Remove cover, stretch the towel over the top of the pot, and replace the cover. Fold up ends of the towel up over the cover to keep them away from the heat.
Reduce heat to very low and steam for 35-40 minutes, until the rice and potatoes are tender.