Nice looking setup
. I have some thoughts but I'm not sure what you've tried...You could cover the tank or part of the tank to gradually kill off the algae. It's better if the die off is gradual so that you don't cause oxygen level issues that could cause a fish kill (seems pretty unlikely in this case but it could be a problem). I would reduce the fish feeding since that's contributing to the problem. I notice the water hyacinths don't look very healthy, are they dead? This makes me think the water temp is pretty low and if this is the case your bacteria in the media beds may not be doing much biofiltration. What's the water temp and what type of fish are you growing?
If your plants are actively growing and the temp is high enough for the bacteria to act, killing the algae by depriving it of light should allow the plants in the beds and the bacteria to use up the phosphates. Without available phosphate the algae will have a tougher time getting a start. You should be able to uncover the tank after this without much of a re-bloom unless you're system is out of balance. Might help to plant more plants as well.
Barley straw is another option that might be worth a try. I've never used it but it has worked for some.
Usually the algae goes away once the system kicks in and never comes back unless to much phosphate gets back into the system water (usually by overfeeding and/or insufficient bio-filtration).
Edit: Couldn't quite understand the narrative on the video although it's probably because of my hearing problems not your audio. I caught that the hyacinth was dead but not the cause.