The 57 watt would be great on a 270g system. Flow is going to be the key.. Just match the flow to the UV unit. I'd target between 1200 & 1600GPH through it.
My UV is on my closed loop off the main display. After servicing my UV, it eliminated the few patches of cyano from my main display. I have some in my display refugium but unlike my main display which is almost completely bare bottom, the display fuge has sand, less flow and rarely ever gets vacuumed. I kind of let that tank do it's thing intentionally and I could care less about the little bit of cyano in there.
In your case, I am sure the UV will help but you should also be vacuuming your substrate very regularly, vacuuming the cycano from the rocks and then blasting detritus off off your rocks on a regular basis. Lastly, cyano normally builds up where detritus and waste settles. This is also the areas of the tank with the least amount of flow. Increasing flow in those areas will go a long way to combating cyano.