As someone who had a long battle with cyano, I can tell you what worked best for me was physical removal of the algae using a siphon combined with increased circulation DON'T scrub it and then siphon as that will likely cause it to spread. Be sure to use only RODI water for you water changes and top offs.
I have never used a reactor, but I have used different media to absorb phosphates. As I understand it, rectors really just direct or force the water through the media. I think there are several people on this board who use the ones made by Bulk Reef Supply.