Although critters like cleaner shrimp and neon gobies are good for keeping your fish clean, they won't take care of ich. The parasites are too small for them.
This is very good news for you! At this point, I disagree completely with any course of action which involves medication or moving your fish to another aquarium. The marine hobby requires an extreme amount of patience to be successful long term. When you medicate, you increase the stress level of your fish. Very often your fish are capable of fighting off whatever the problem is without any intervention on behalf of the fishkeeper. There is no chance that I would medicate if the only symptom was flashing against the rocks.
It is very possible that you have the beginning of head & lateral line errosion, and not a parasite at all. The Coral Beauty scraping its face against the rock is a strong indicator this is likely the case. Centropyge angels are usually one of the fish species to show signs of HLLE and it usually begins around the head. I honestly do not see anything which you describe that even begins to resemble ich. Please do not use copper! Don't get me wrong, you could have ich, but you are not describing any of the primary symptoms yet.