The cyano is making use of a niche in the tank that you're providing.
IMO that niche has more to do with available nutrients than it does with other factors.
And by nutrients, I'm not talking about NO3 or PO4.
I'm talking about other nutrients (e.g. K, Fe, Si, etc) being in excess of available N or P.
Cyano tend to have ways of utilizing forms of N and P that aren't so useful to other plants, so in turn they can sometimes utilize other dissolved nutrients that may be unavailable to corals and other algae which may be effectively N- or P-limited (or both).
If this tank experienced a crash, then it's likely that there was a considerable amount of bio-mass both on and within the sand bed. Phosphorus and nitrogen would be likely to be either limited or unavailable in dead matter, but other nutrients and minerals would probably be more available.
A hard core gravel vacuuming or (more simply) a sand bed removal|replacement may do a lot of good. Blast the rocks with a powerhead too if they are also "nasty".

Remove as much material as possible during siphoning.