I would definitly address the cyano. If you got rid of it and its coming back, you may need to address the cause rather than just the bacteria.
I had a small outbreak in my sump some time ago. I isolated the sump from my DT and treated it alone. I had to move my heater into my DT but that was about it. I shut down my return pump, turned off the skimmer and dosed chemi-clean. it was gone overnight.
If you do this I would do a substantial water change after the treatment. And follow that with another one. Youve got to lower your nutrients to beat the cyano.
Are you using RO/DI water?
Your chaeto will consume nutrients but youve got to start with decent water conditions to allow the chaeto to take hold. once it starts flourishing, it should continue and will become a vital part of your nutrient export.
A lot of folks seem to struggle with finding just the right light to grow their chaeto. Tho I think a lot of them are adding chaeto to a dirty system to try to "fix it". I believe your better off if your tank is fairly well under control when you start chaeto or it may die just like everything else.
check out the link posted by mfinn. I would choose the light on the right in the pictures. My LFS tried to sell me a $200 "refugium fixture" Bahh! I have chaeto growing out my ears
Kill your cyano and things will be easier.