I've have never fragged a cyphastrea. I have one that has grown into the plug and I would like to pop the original fragged off the plug and glue it to a rock. Will the surrounding growth survive?
If you're careful yea it should. Use a chisel and hammer, or something similar, and give it a good quick strike to break it free. I just did my meteor shower for the first time, pretty easy if you find a good spot to break it lose.