My two cents, Stripping out the phosphates hurts corals a lot worse than it hurts algae. And keep in mind amino acids are one form of organic nitrogen and by dosing them when PO4 is undetectable runs the risk of creating an N

imbalance that can cause bleaching. If this was my tank I would be adding some fish as fish poop is an ideal coral food and just using manual removal for the algae. It's seems a sure bet to me the microbial processes have been pretty messed up. Corals will correct that eventually if and when they recover but I would be proactive and do some water changes with water from a "healthy" reef system. To help get a better understanding of microbial processes in reef ecosystems a good introduction is Forest ROhwer's "Coral Reefs in the Microbial Seas" (kindle $10, paperback is $20). Here's some additional links if you're interested:
Phosphate Deficiency:
Nutrient enrichment can increase the susceptibility of reef corals to bleaching:
Ultrastructural Biomarkers in Symbiotic Algae Reflect the Availability of Dissolved Inorganic Nutrients and Particulate Food to the Reef Coral Holobiont:
Reef building corals associated with symbiotic algae (zooxanthellae) can access environmental nutrients from different sources, most significantly via the up...
www.frontiersin.org
Phosphate deficiency promotes coral bleaching and is reflected by the ultrastructure of symbiotic dinoflagellates
Enrichment of reef environments with dissolved inorganic nutrients is considered a major threat to the survival of corals living in symbiosis with din…
www.sciencedirect.com
Effects of phosphate on growth and skeletal density in the scleractinian coral Acropora muricata: A controlled experimental approach
Phosphate contamination can negatively affect corals, modifying growth rates, skeletal density, reproduction, mortality, and zooxanthellae. We determi…
www.sciencedirect.com
High phosphate uptake requirements of the scleractinian coral Stylophora pistillata
SUMMARYSeveral untested aspects of the regulation of inorganic nutrient uptake were examined using nutrient depletion experiments with the symbiotic coral Stylophora pistillata. The total inhibition of phosphate uptake in artificial seawater lacking sodium indicates the involvement of a...
jeb.biologists.org
Coral and macroalgal exudates vary in neutral sugar composition and differentially enrich reef bacterioplankton lineages.
Increasing algal cover on tropical reefs worldwide may be maintained through feedbacks whereby algae outcompete coral by altering microbial activity. We hypothesized that algae and coral release compositionally distinct exudates that differentially alter bacterioplankton growth and community...
www.ncbi.nlm.nih.gov
Sugar enrichment provides evidence for a role of nitrogen fixation in coral bleaching
onlinelibrary.wiley.com
Pathologies and mortality rates caused by organic carbon and nutrient stressors in three Caribbean coral species.
Starch and sugars (doc) caused coral death but not high nitrates, phosphates or ammonium.
Global microbialization of coral reefs
Analysis of 60 sites in three ocean basins suggests that overgrowth of fleshy algae on coral reefs supports higher microbial abundances dominated by copiotrophic, potentially pathogenic bacteria via the provision of dissolved inorganic carbon.
www.nature.com
Here's a good video put out by University of California
And "Changing Seas"