Carbon is an oft-overlooked parameter since we can't really test for it that I'm aware of.
As I understand it, nitrates and phosphates are not necessarily toxic to coral at the levels most of us keep them. They are a nutrient to coral. The problem is they are also a nutrient to algae. We try to limit nitrate and phosphate not because they are toxic to coral necessarily, but because we are trying to limit algae, which compete with coral.
The same applies to carbon. It is not necessarily toxic, but it helps algae out-compete coral.
So while phosphates are officially high, I don't know that knocking them down is all you will need to do if you're not also limiting/exporting carbon in some fashion.
How to limit/export carbon? Algae grazers, GAC, UV, & aggressive detritus removal via mechanical filtration & water changes. I also can't recommend sulphur denitrators highly enough; I'm amazed they aren't more popular.
Some people feel that mechanical filtration & reef tanks don't go together because of the prevalence of filter feeders in these tanks. I used to share that opinion ("mechanical filtration is a nitrate factory!"), but not any more. Now that I understand that nitrates are not necessarily the boogieman they are made out to be, along with a greater appreciation for the negative effects of short-chain carbons in the water column, I feel that the benefits of capturing detritus via sand-stirring & mechanical filtration outweigh the negatives of the possible excess nitrates caused by a mechanical filter. ESPECIALLY when combined with a sulphur denitrator.
FWIW, I broadcast feed zooplankton and phytoplankton and oyster tissue twice a week, so my filter feeders are getting what they need despite the mechanical filtration.