I have a really bad green hair algae problem in my new 1 month old 3G picotope, its covering about 50% of my rock. After the initial GHA bloom after cycle I added a CUC of 3 astrea snails and 3 striped trochus snails, they haven't touched the stuff! All parameters are showing 0 as well.

So i've cut out lighting out completely, added chaeto to my sump, and started dosing Mg. Is there anything else I could do? Can somebody give me a suggestion on a good GHA CUC lawnmower?

your tank is a month old. this is a normal stage of the nitrogen cycle. RELAX! it should go away in time.
I would stop dosing the Mg, because it is such a small aquarium, and you could really screw it up if you overdose by accident. In regards to a cuc member, I would look into star astrea snails. They eat pretty much everything, and they look awesome. Much better than an emerald crab.