The algae isn't growing because of high nitrate or phosphate. It doesn't work that way. You have way too much light, to start with. You have almost 5 watts per gallon, where about 2 is all you need. If your lights are suspended above the tank a foot or so, that comment isn't correct, but if they are right at the top of the tank it is. How do you get the CO2 into the water, and how much do you maintain in the water? This actually looks to me like low CO2, with the plants being stunted by not having enough carbon to grow at the rate the lighting is driving them at.

If your "heavy plants" is anything like what I just had in my 45 gallon tank, the mass of greenery is also interfering with water circulation, which keeps the CO2 from reaching all of the plants. Do you use a powerhead in addition to the filter to better circulate the water?