The coral should recover.
Engineer Gobies are interesting but a real hassle.
The Pop Bottle Fish Trap works just as well on them as it does on any fish. I use fishing line in three places to tack the two pieces together with a long length of fishing line to make it easy to lift up from the bottom.
Place a rock inside to keep it on the bottom. Place in it a solid piece of food and put it in position at night. By morning there will be fish inside, though it may take up to a week for them to get used to it's presence in the tank.