+1 on chaeto
I see your nitrates are at a decent level, but Phosphate is very low (zero). There are articles out there suggesting that low nutrient environments are breeding grounds for cyano. They out-compete other micro fauna under those conditions.
I implemented an algae refugium (ulva and chaeto) and dramatically reduced the bubble algae in my 135 gal DT (mixed coral, medium fish stock, heavy feeding, deep sand bed, SB Reeflights + 2 Jabeo wave pumps) and saw some reduction of bubble in my detritus laden frag tubs connected to the DT.
Then, my Nitrate and Phosphate fell to non-detect levels (Red Sea Pro and Hanna ULR). That's when cyano started showing up on my sand bed and low flow regions of my live rock. I did siphon the sand 2-5 times in those regions to try to pull trapped detritus out. I removed much of the detritus from my frag tubs. That helped to remove about 80% of the cyano from the DT with several live rock spots remaining and one spot on the sand. After seeing the BRSTV episode on ULM pertaining to nitrate dosing, I decided to dose nitrate, Ca(NO3)2 and phosphate, Na3PO4, on a daily basis with a dosing pump. About a week later, my sand is free of cyano and it is slowly fading from my live rock and is mostly gone from my frag tubs. My phosphate is now about 0.040 ppm-PO4 (13 ppb-Pi) but my NO3 is still non-detect. I know NO3 is in there because I'm adding it everyday, but something (algae, coral, other) are consuming it.
My recommendation: add macro algae (e.g. chaeto), bring phosphates up by first stopping phosban and if necessary implement regular PO4 dosing. You don't need a lot of PO4, just try to hit 5-10 ppb-Pi (0.015 - 0.30 ppm-PO4). Your nitrate is probably fine where it is, but chaeto will probably take it down low.
