The balance between nitrates and phosphate is important. So post the readings.
You have done a lot right. Often the learning involves taking one step at a time. Buy some new plants and restart trying things out.
I too have a diatom problem. My tank has been set up for 8 months. I figured out my tank gets dirrect sunlight for about half an hour on sunny days. Since I can't move the tank I bought a bristle nose pleco. They eat algae and stay small - 6 inches. That solved my problem. A pleco may not solve your root problem, but your tank will be spotless and the pleco will have a never ending supply of food.
Another idea -maybe you need some fast growing plants and dose more regularly with ferts and especially API booster. I dose everyday with booster (I have low tech tank) and found it helped my plants and slowly has gotten rid of all my algae issues.
Lighting- how deep is your tank?