Just a Few Side Notes
I'm just now making myself aware of high PO4 in my system that my scrubber cannot handle alone. So GFO will be attempted to get parameters closer to what 'may' yield better results.
GFO should solve the problem in the short run but if your ATS is there to get rid of excess waste then I think that you should also go back and look at your ATS to see if it is undersized, has too little flow or light. The more variables that you add to a tank, like other export methods, the harder it is to diagnose and keep stable.
When I hear that someone is having issues with P and not N, I think that PERHAPS the ATS is nitrate limited and there are threads for that, primarily for people with skimmers that are dosing Vodka but ATS users can have the same problem. I had them when I tried vodka.
As for waste exports, I think that if you had a good enough skimmer and plenty of GFO, you would not have to worry much about poo. [Of course you want to get rid of as much as you can. (repeat)]
The reason that I say that is that I had tank with a well designed ATS and a popular version of a Jaubert sand bed with a plenum. As I have detailed in other threads, the solid waste was processed.
I could see into the open water volume at the bottom of the tank that was stagnant. On the glass, I had placed a coated magnet so that I could move it around. In the first month there was a ¼ inch fine layer of gray dust like detritus that formed on the bottom. Eight years later that layer never got any thicker than that same ¼ inch. It had to be different dust.
I was growing filter feeders. I put food in the tank daily that was measured in spoons and ½ cups, not cubes. The poo, un-used powdered foods, living and dead bacteria, fish foods, fish fertilizer and many other things went somewhere.
Between my export and tank processes my N and P where hardly ever even detectible. I would suggest that food web processed it. Dr. Adey wrote a lot about this web in his book in the early 90's. Recent studies are showing that the web is much bigger and more complicated than we thought and is still, little understood.