The only silver lining that I see is that Rotenone is an option. GS are more susceptible to it than other species of fish, so you might be able to get a lethal dose of it in there for them and not harm the majority of the other fish. It'd be a thin line you'd be walking.

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3/4 to 1 1/4 ac pond LMB, SMB, PS, BG, RES, CC, YP, Bardello BG, (RBT & Blue Tilapia - seasonal).