I'm currently on this quest as well when my nitrates hit 60 and phosphate 0.9 a couple months ago and my corals started suffering. This hit me out of nowhere because historically my tank has been low nutrients without much filtration, only skimmer. So far in the past 2 months I've added a filter roller, dose DIY nonox (vinegar + vodka), skimmer running wet, and water changes. Its only gone down to ~40 nitrate and 0.4 phosphate so still a ways to go and nothing has been the silver bullet yet. Next up I'm setting up a DIY turf scrubber to see if that helps. I want to avoid last resort which is reducing fish population or feeding less.
I might be hitting the point of Old Tank Syndrome
How are your corals suffering? What are you seeing?