I have a similar situation. I have a green hair algae problem in my FOWLR tank. I have a puffer and a trigger so I am limited to clean-up crew. I bought a lawnmower blenny to help with the algae. I guess he's on strike because he has no desire for the green stuff. He munches other types of algae like on the glass and fake corals I have. Then I tried a fox face because I was told and have read they are good for eating algae. Same deal he is more interested in the meaty food I feed my trigger and valentini puffer. As a last resort hoping the trigger won't eat him, I recently bought a pin cushion sea urchin. That thing cleans up house. Almost all the green hair algae is gone and the fish leave it alone (SO FAR).
I would recommend a sea urchin, but I am not sure if they will munch on your corals or not. I have read mixed feelings about that. Good luck.