1/16" though? That sounds gargantuanly large for black ick? I thought black ick looked like a light dusting of fine pepper grounds?
If it is the same thing I'm thinking of, a freshwater dip works quite well since it's an external parasite. I had a yellow tang get this, several several years ago, shortly after I purchased him. I made up some FW, matched the temp to that of the tank, and he sat in there for maybe 4 minutes. The spots literally fell right off when I put him back in the tank and they never re-appeared.
But I don't know if I'm thinking of the right thing. It's not the normal ick, a FW dip doesn't cure that one.
Sorry can't be better assistance. I would have thought "black ick" from the get-go but it's the size of the dots that's thrown me off...