Algae die off is generally about limitations. If there is no nitrate in your tank, your algae will die off. If there is no phosphate in your tank ditto. (When it reaches a happy medium, that is import of nutrients = consumption you get a reading of zero) There is another major nutrient, (nobody tests for the minors so I won't bother), but that is iron. If your aquarium is iron depleted from the turf algae growing too fast, it will wither or will not grow anymore and nitrates and phosphates will continue. Based on Liebig's law of the minimums, the idea is simple, for example if your car needs four tires to run, and you have only 3, you can't drive, no matter how good the condition of the other 3 tires. (He did it with a barrel, can only fill it to the highest hole - well stave but anyway here is a
link.) If it is your turf algae, than one of those 3 things , (assuming light is not a problem) is likely your culprit. If one of those is missing, all the flow and additional light won't solve a thing.
The other likely scenario is that you have a bacterial bloom. A long term solution to a bacteria bloom is a skimmer, which removes free floating, (not the desirable benthic), bacteria. The quick fix is a decent size water change and to run carbon. The long term fix if you run into a chronic problem is a protein skimmer. With proper husbandry, a protein skimmer will not be necessary, but it can be useful.
So before you remove the ATS, do multiple water changes and run carbon until the tank clears, and then see if the problem comes back. If it does, then experiment with removing the ATS, doing water changes and running carbon and see if it stays clear. If it doesn't try a skimmer.
Edit - Oh well I should have just checked your gallery. You are running cyano on the ATS, cyano doesn't need iron to grow, so you can skip that portion. Try the water change and carbon, that should help with the bacteria bloom.