I think a big problem is going to be the stuff that is rotting in your rocks and not getting taken out of the system.
If you 've overfed which you stated that you have it takes a long time for all that food to completely decompose and be skimmed and filtered out of the system.
You say you're testing Nitrates at 20 which is after you take into account the nitrates the algae is using to grow.
My recommendation would be to get some rubbermaid bins and take out all rock and wash them off in one bin of saltwater to get all the crud out then leave them in some more bins full of saltwater.
After all rock has been removed siphon the water out of tank while removing all fish and creatures left into another rubbermaid bin.
While siphoning this water into the bins make sure you have some filter floss on end of hose to filter out crud in water.Once you remover all the water down to about 1" inch of the sand you should be good.
( If you remove all the water and vacuum sand you will kill alot of good sand dwellers that you don't wanna kill)
This should clear out almost all of the the rotting stuff you have in there that I believe is giving you these problems.
I have done this multiple times in my 125 6 foot tank and it has been very effective at getting rid of nitrates and phosphates and I have never lost a coral or fish.
The water that I washed the rocks off in by shaking them was nuclear green by the time I washed all the rocks.
I can almost guarantee that by what you've said your problem is rotting food and waste that is not getting taken out the system.It is being left to fully decompose and therefore polluting the tank slowly over a long period of time.
A less effective but easier way to help would be to blast out all your rocks with powerheads and a turkey baster then use some HOB filters with floss or spongers to filter out the stuff you blow out of rocks.After a day or so of use and your water is clear take off filters and garbage floss and rinse out sponges.
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