undetectable PO4 (assume you are using a reliable test kit) I think is your culprit. Nuisance algae/bacteria can be more resourceful than corals, so they flourish while your corals struggle.
You posted that you are thinking for switching from GFO to pellets. If your PO4 is zero, seems to me it makes no sense to run GFO.
Zooxanthellae in your corals need both NO3 and PO4 to make the sugars for the corals. If there is no PO4 then makes sense that your corals and Cheato will not be using up NO3 du to the lack of its partner for photosynthesis. If you let PO4 rise, you may very well see NO3 drop as your corals and cheato do their thing.
Cut the GFO and only use it to control PO4 when it goes above your target numbers (you didn't post your target numbers so I recommend if you don't have targets to do so - Red Sea has good articles on this , they suggest PO4 at 0.08 - 0.12 ppm for mixed reef tanks with NO3 at 1-2 ppm).
Pellets can be tricky, I would not do that until you see where the tank NO3 and PO4 balances after you stop stripping the tank of PO4. If you still need to carbon dose, Red Sea NOPOX is more precise/predictable.
Also, read
@brandon429 thread on how to clean your sand and rocks of detritus and algae with H2O2 and elbow grease scrubbing. He will even let you start a cleaning thread to guide you through the process and document your progress.