Moving an Elephant Ear
Take a very sharp razor blade, and cut it off the rock as close to the base as possible. It will puke some stuff out -- don't worry about it. Leave it in tact as best you can. Set it in a quarantine tank with light or other region with VERY LOW flow and some light for a week or two to let it recover. If you use a QT tank, change the water often (but slowly) with new water from the main tank. It will recover just fine. The bits left on your live rock may well grow back to new mushrooms in time.
If you have already angered it, you might want to let it recover for a week or so before doing the main operation.
-Greg