Something else is happening that you need to figure out. Chaeto cannot outcompete bacteria nor dinos (zoox) since it limits at a higher concentration. If the chaeto and other algae is growing, then there is enough there for the bacteria and coral. Bacteria can outcompete dinos, but in natural situations, the bacteria are deep in the sand and rock, but this can change with organic carbon dosing. Like I said before, though, if you are carbon dosing, GFO, LC, etc. then this can alter the equation dramatically. It is possible that if these tanks are new(er) or just had dry/dead rock get cleaned/cycled, then the aragonite is binding up all of the phosphate - never underestimate aragonite's ability to bind phosphate and both keep it really low in new tank (until it binds enough to leave some in the water) and also be quite a reservoir in water with high concentration levels.
OP - if you think that this is a bacterial infestation, there are threads that I have seen where people treat with an antibiotic - search for "STN and antibiotic". This is the one that gets thrown about a lot. It is a dense read, but might help you out. Good luck.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4083779/