you can move the mushrooms, I just did it with some in my tank.
first get the mushrooms to close up as much as possible.
I used a pair of frag shears to cut the rock away from the base where the mushroom is attached. You want to scrape under the mushroom so there is still some rock attached to it. this will be just a thin layer of rock, nothing large. you may then use a drop of glue where the rock is to attach the mushroom somewhere else.
you may use this same method with any soft coral, when working with zoa's be extremely careful, use protection, as they contain dangerous toxins.