Verti,
My only concern with the provisional diagnosis of flukes, is that I never have seen Neobenedenia on a fish unless it was right on its eye, or had been partially dislodged by some treatment. Maybe you are just more observant than I am, or can get a closer look at the fish? Normally, Neobenedenia lays tight agains the fish's body and is so clear as to be invisible.
Anthias are certainly one of the species that can develop Neobenedenia.
Do the worms move around or do they always seem to be in the same place on the fish?
Jay
Jay