There's a lot more going on in a reef ecosystem than just inorganic forms of nitrogen (ammonia, nitrites, nitrates) and inorganic phosphorus (PO4). I would be doing water changes and siphoning out nuisance algae with the water changes. Water changes will remove the hydrophillic labile Dissolved Organic Carbon (DOC) that promotes pathogenic shifts in coral microbiomes. Thsi labile DOC will also allow heterotrophic bacteria to feed off the refractory DOC that builds up in a system without water changes and can drop oxygen levels in coral surface mucus layer suffocating corals. Here's some links you may find informative. (Adding bacteria won't hurt but keep in mind less than 2% of microbial stuff can be cultured and stuck in a bottle and sponges and corals are processing nitrogen as well as phosphorus and carbon.)
"Coral Reefs in the Microbial Seas" This video compliments Rohwer's book of the same title (Paper back is ~$20, Kindle is ~$10), both deal with the conflicting roles of the different types of DOC in reef ecosystems. While there is overlap bewteen his book and the video both have information not covered by the other and together give a broader view of the complex relationships found in reef ecosystems
Changing Seas - Mysterious Microbes
Nitrogen cycling in hte coral holobiont
BActeria and Sponges
Maintenance of Coral Reef Health (refferences at the end)