Im not sure if it will work with shrooms, but with my invading xenia, I but a torch coral by it and it stung the hell out of the xenia, and in a week the whole patch by the coral was dead.
I'll take some also but back to the point. Couldnt you just increase the flow where these shrooms and sps is and make the mushrooms detach? from what I know shrooms dont seem to like alot of flow, just aim a powerhead at it. May take a lil while but atleast you'll know you didnt have to kill some pretty mushrooms to save another coral