Is there a healthy way to grow green hair algae in the tank? By healthy, I mean is there a way to grow green hair algae in the tank without ruining the water quality first to grow it?

The reason I ask is because the grazers in my tank look hungry... and possibly even the snails too.

I'd be best to grow some macro algae that they'll devour rather than ignore (like hair algae).

Try getting some Red Gracilaria (aka "Tang Heaven") or even Cheato which many fish like.

Bob

I have the chaeto... now I just need the tang. I don't think my dwarf angel cares for the chaeto though.

Derbesia marina is growing in your tank right now, you just can't tell because it is being ground down as soon as it appears by the actions of your herbivores. Derbesia will grow in very clean pristine conditions too if there is nothing present to eat it, it will grow. The real issue is that you have just the right number of snails to keep its growth imperceptible but not so many that they don't get enough to eat. Snails also eat diatoms and the tiny initial growths of filamentous reds, browns, Enteromorpha, etc. but only when it first appears as a film. Filamentous algae of any significant length they usually avoid so the only way it benefits them is if it is grazed down to the rock on a regular basis.
Tangs can be fed algae sheets, romaine, and algae based frozen foods soaked in Selcon to keep them healthy.

Try putting some smaller live rock into a small tank and "culturing" it. Put the tank in direct sun and put a handful (not really) of flake food in. Give it a couple weeks or so and there should be some usable algae. Then just put the rocks in the tank. You can rotate pieces through to have a more constant supply.