You should siphon out as much as you can each water change too. Don't blow it off rocks. Cyano
doesn't need much to thrive like said before. I had dealt with it for 6 to 8 months. Still have some now but manageable.
I did all this and not sure if one thing did it or all.
Lower hours of day light by 2 hours( temporary)
Covered a window by tank better. Less direct sun light.
Bigger and more frequent water changes. Siphoning out as much as possible.
Ordered Cerith snails. Heard they will consume it
Chemi pure elite I think helped with parameters.
Just like you I have un detectable phos. Only 10ppm of nitrates at most. Now down to under 5ppm.