Mushrooms

Cut off as much as you can, heavily shade or paste the rest.  I'm told that the usual non-biological methods for aiptasia/mojano issues work, although I would do them in a couple stages. Edit: Chipping them off always works too.
 
Then you need to shade them farther.  I've seen it done with 12" square tiles.  I suspect a black garbage bag folded over several times then held in place with zip ties for a month or so would be a strong deterrent, especially if they were sliced of with a blade first.I've seen people use reef putty for zoas, but that takes a lot of putty.  Just be aware that they may try to detach and float elsewhere.  They'll do this on occasion anyways, but if you catch them when they start you can always chip off the offending mushroom with a chisel and a hammer (or a cheap screwdriver).
 
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