Six line wrasse eats ich off other fish????

[Kabong]

Can't say I've heard of 6 lines eating Ich myself, But even if yours does.
I doubt it would be able to eliminate ich from your tank.
Also taking the tang out to treat wouldn't solve your problem either.
Part of ich life cycle is an off the fish, So you take the fish out cure him of ich, put him back in the tank and hes got ich again.
Just because you cant see ich doesn't mean its not there I'm afraid.
Basically your option's are QT and treat all your fish for over a month.
Or live with the fact that you have Ich in your tank and try to solve what the tangs issue is.