I'm not 100% sure about this, but I'd be willing to bet I have it right.
Cyano is not an algae, its a bacteria bloom and therefore your lights have no effect on it. I'm not convinced at all that dosing H2O2 will help either. I have a small algae issue and if I dip a rock in typical 3% H2O2 for 3 to 5 minutes, the algae dies. Zoas are really upset and slime like crazy, but are fine after a few days. I took a couple of small rocks with a small amount of algae on them and put them in a 5g tank. I started dosing 1ml/g for a couple of weeks and the algae grew. So I upped it to 5ml/g for 2 more weeks and the algae still grew. I upped it to 10ml/g and I think the algae growth may have slowed after 3 weeks, but it's certainly not dying off.
But your issue is bacterial not algae. Suck it out with a turkey baster or a siphon and add more flow the the area. Be careful what you add and feed to the tank, bacteria like carbon.