Sorry your fella isn't well, its hard to say what is wrong, however, if you are not adding any minerals to the R/O water-he could be suffering from the long term effect from that and possible poor nutrition.
What I would recommend-is getting some dechlorinator and start making 25% water changes with a 50/50 mix of your tap water and R/O water-along with the proper amount of dechlorinator. Make these water changes every 15min for about an hour or to his tolerance today. Then lower the water level by half and make 25% water changes daily for a few days using the 50/50 mix. Then re-eval.
Nutrition-good quality varied diet fed in small frequent meals and if you have access to any live mosquito larva-offer several rinsed a couple of times a day to boost protein/nutrition intake to support the immune response.
As for the surface/protein scum-generally this is not uncommon in unfiltered tanks. It is usually caused by either the fish food, other organics in the system, something on your hands or it can be due to the environment itself. Using the paper towel the way you are doing is about all you can do-As long as the surface scum doesn't get too thick to impede gas exchange within the system-it shouldn't be problematic for the Betta.
Good luck and keep us posted....