It's not your heavy bioload that helped, it was the 3 tangs.
First, I haven't always had 3 tangs in this tank. The 3rd went in about 7 weeks ago. Hippo tangs are NOT algae scrubbers the way other Tangs are. The Yellow, nibbles all day but can hardly be the single source of missing algae.
I'm sorry, but your thought does not hold water.