Don't panic. You've got this.

I just went through your entire thread and realized we never discussed metals or iron, at least I didn't see it. For you to say that staining is getting worse with the elevated FC level would seem to indicate you have some metals in the water - usually iron or copper. Iron is common from well water, but some city water sources are a bit high in iron too. Copper comes from mineral sanitation devices like the Frog System, but also from many, many pool store chemicals and algaecides, or products with the name "Blue" in them. For now, continue with the
SLAM Process to make the water clear and algae-free.
As for those pesky stains, do the following please. First, share with us a pic or two of the stained areas. Next, grab a typical Vitamin C tablet and rub it on a stained area. Let me know if it lightens up that stain at all. When was the last time you cleaned that cart filter? Did you see any light blue/turquois colors on it?