It usually doesn't work that way. Unlike real algae, cyanobacteria can't be "outcompeted" by plants. Adding NO3 is one factor that will keep them in check and generally reduces the risk of outbreaks. Larger water changes, vacuuming the substrate, added circulation, filter cleanings are other factors. None of that kill BGA. Some say a dark period (blackout) for a few days, or H2O2 treatments help. Not in my experience.
If it doesn't go away, in the end you may have to resort to an erythromycin treatment to get rid of it. Seems like the BGA isn't really taking over (yet), so see how things develop in a couple of weeks from now.