All good advice. What I would add is to stay away from that 10000k bulb & run 6500-6700k only. BGA will thrive on most spectrums except 6500-6700k spectrums.
I had a big problem with BGA & changing bulbs to 6500k helped a lot. I next added carbon to my canister filter & let all my canisters blast without a spray bar. The carbon is good at controlling DOC's which the BGA will feed off. The carbon is only used during the BGA battle . After it is gone take it out , but You may have to change it out a couple times until the algae is gone. When your tank cycles fully you can try the 1 day blackout with antibiotic if it is not gone. In my case all the elements mentioned were needed to kill it off since it was very viral in my case. It lasted for months until I changed my bulbs, added carbon, blackout with flagil antibiotic & added flow. The nitrates need to stay above 10ppms or you will never get rid of it. That being said you must keep all the nutrients up as well as CO2. Pressurized CO2 will be best at least 16-38 mg/L of it. Nitrates can never crash or it could come back.
My tank has been BGA free now for 3 months & the water is crystal clear without any sign of algae on my plants or even glass.
I would cut your tank with r/o water to get those incoming nitrates down to near zero. You did not mention what your Kh was or Gh. If your Kh is high it will be difficult to get enough CO2 into the water. High Gh could be a problem as well. Make sure to add Gh booster if the opposite.
My 2 cents