I think I see coralline algae growing on the glass which is good.
But with nitrates at 20 ppm.. and phos only at .03 ppm that seems odd. I would expect more phos.
Running carbon is fine. I tend to run it quite often and refresh it once a month. It cannot hurt. Adding gfo with only .03 ppm is ok I guess. I would only use a 1/4 cup I suppose. Just a touch on top of my carbon in a reactor.
But I do agree SPS are having a hard time. Having algae actually grow on them is a sign of too much nutrients in the tank. I would keep doing weekly water changes until nitrates are at least down to 1-2 ppm. At that time I would see if they rise again doing your normal routine. Only when you can keep nitrates steady at that lower level would I try SPS again.
You also own lighting that has the ability to fry new coral, fyi. I do not use LEDs but I would wonder what the par level is for each of those SPS.. versus what they were kept under before. I doubt that is it.. but worth exploring. Maybe you have them on high?
I realize what I am stating is not set in stone but on a new tank it seems to be a reasonable goal to shoot for. Lower nutrients like nitrates to a much lower level.. keep them stable at that low level with normal practices/routine.. and try another coral again like montipora digitata or a cheap acropora frag.
This is all part of the learning curve. Don't give up. Often in reefing the time it takes for a tank to mature can be like magic on coral health. 1-2 years is where things can really take off stability wise.