I'll let Pooldoc come back and continue with his advice, since he's the one with the manganese experience...but if the cup of chlorine didn't really mess with your water, then at least you know you can keep very low levels of chlorine in the pool now to keep algae from making the situation worse. Until you add stabilizer to the water (and you're not at the point to do that yet, I don't think), the sun will rapidly consume the chlorine you've added, so you may need to add bleach 2-3 times a day just to keep "some" chlorine in the water. The sand filter will be much easier to deal with than the cartridge, I think, so I think that ws probably an ok move..

Janet