Reduce your lighting maybe for a few days, how long do you leave kyour lights on for? And yes snails are the way to go, they will clean it up. You could also consider reducing your feeding as well.
Hairy green algae will grow just fine in low light and low nutrients.
What keeps them at bay is competition (coralline algae, macro algae and corals) and algae eating inverts (hermits, snails, amphipods,...).
So far, fish have been totally ineffective for me to eliminate hairy algae. All they may do is keeping them short.
I have two 10g tanks next to each other:
One has a S. gigantea, a pair of percula, a large pair of banggai cardinals, a pistol shrimp, a pair of yellow banded cleaner shrimp and a quickly growing colony of green star polyps. On algae eaters are there: one turbo snail (were 4 but the other 3 were eaten by the gig) a handful of blue-legged hermits, a growing number of stomatella snails and an army of amphipods. On the two live rocks grow a couple of coralline algae and caulerpa.
This tank sits straight under a Kessil A360WE at full intensity and 80% color and the fish and anemone get fed a ton. There are no hairy algae in that tank (with the exception of some on the inside of the skimmer). The only pest right now are cyanobacteria.
The other tank is a QT with a small pair on banggai cardinals, an orchid dottyback female and a bicolor blenny male. No snails or hermits in this tank and the decoration is a good load of real reef artificial rock. The fish get fed sparingly and the tank gets just the stray light from the Kessil.
Still, hairy algae are thriving in this tank.
