im not 100% sure but a cheap solution would be to buy/try just the bacteria replacement filter for a aquaclear filter. its like $5. It removes the nitrates in the water. The reason why plants work with reducing alge is because they compete with the alge for the free nitrats in the water. I have a few fish takes with fish and these bacteria filter seem to keep my water crystle clear and i have 0 alge. good luck.

the only downside is that the bacteria filter/bag needs to sit in the water.but u can hide it with rocks.

its somthing to try for 5$