The photo and that information help. The light is a bit high in the blue spectrum (the 9000K), while the 6500K is perfect. Are there two sections of diodes that can be replaced individually? I looked this unit up online and it wasn't clear. If you could remove the 9000K section and replace it with either another 6500K or a warmer light (lower Kelvin number is more red, warmer light) it might help. High blue light does encourage algae, so this would be one way of thwarting it while improving the plant growth. Plants need red and blue light in order to photosynthesize, and red is the more important of the two. 6500K light is high in red, blue and green, and although the green does not drive photosynthesis, it does improve plant growth, probably because of the greater intensity, and it is closest to mid-day sun.
Moving on from the light itself, the duration is fine. Floating plants would help here. Water Sprite, Tropical Frogbit, Water Lettuce are three good floaters. These will reduce the light thus impeding algae, and they are incredible "ammonia sinks" because of their high uptake of nutrients including ammonia. This should not harm the lower plants, but it can again thwart algae.
Now to the fertilizers. These products came up on another thread earlier today, so I had a look at them then. The TNC Complete seems OK, my only concern is it does have phosphates and nitrate in it. Neither will really help plants, but both again encourage algae. There is never a shortage of phosphates in an aquarium because the fish foods contain all the plants will ever need in a natural or low-tech planted system. And nitrate is not needed because plants prefer ammonia/ammonium as their nitrogen source, and they take up a lot of this. The TNL Lite has everything except these two, so that might be worth looking for.
The TNC Plugs are probably worth getting for the swords (left rear) and Vallisneria (right side) especially. Both of these [plants are heavy feeders, and from my experience they really benefit from direct substrate tab fertilizers. I use the Seachem
Flourish Tabs, but the TNC Plugs seem similar and for all I know may be just as good. The thing I also like about the Flourish Tabs is that they do not leech nutrients into the water column, which means algae cannot use them. The TNC Plugs may or may not be similar, they do say the nutrients are released over six months to the plants' roots. Up to you which, but I certainly recommend substrate tab/plug fertilizer for these two plants, well worth it.
Last the TNC Carbon...do not use this. It is 2% Gluteraldahyde (and water), and Seachem's Flourish Excel and API's CO2 Booster also contain this highly toxic disinfectant. It is used in hospitals to disinfect surgical instruments, in embalming fluid, in ships ballasts to kill bacteria...this does not belong in a fish tank. It does over time impact fish. There is CO2 continually being produced in any fish tank, not just from the respiration of fish, plants and many bacteria species, but primarily the breakdown of organics in the substrate. With your light on six hours, you should not run out of CO2 in that time frame.
Feel free to question anything.