I had to deal with phytoplankton blooms several times and I know nothing better than UV. Many years ago I tried to kill a dinoflagellate bloom (brown water) with lights out. After showing no signs of decline after 1/2 year just with room light I finally eradicated it with UV. I had green water from Nanochloropsis recently and I guess there is no natural cure. Also nutrients don´t have to be high to inititate such a bloom. I think the cause are instable conditions, I only had these problems with freshly setup or young tanks. Water changes don´t help. They do not stabilize conditions rather the opposite, they introduce fresh nutrients and the unicellular algae divide so fast you have the same bloom or worse in just a few days. You also can never get all the phytoplankton out except by emptying and sterilizing the complete tank and if you have bad luck and you use some tool or introduce one coral of the old tank you reintroduce the phytoplankton and initate the next bloom.
I had copepod blooms while clearing a dinoflagellate bloom. Logic would say next time just wait until the copepods have eaten up all the phytoplankton but this never happened yet. They only ate up blooms in the process of clearing maybe eating dead cells or other organisms that degrade the dead cells like thraustochytrids.
In my opinion only UV will help.