That's a tough predicament. Judging by the color of the corals, there is certainly not a nutrient issue. I wonder what is feeding the cyano. Have you tried moving power heads around to create more flow in that area? That looks like it may be a low flow spot which could be a factor in the cyano there.
I battled cyano at one point and it would not go away regardless of what I tried (low nutrients, increased flow, etc...). I did one treatment of red slime remover which got rid of it and it has never come back. I would do that only as a last resort, although I experienced no ill effects from it. But, I always prefer to correct things naturally if possible.