Peer reviews and other comments on the sea bird article seem to indicate that what allows the birds to thrive is what makes the reef more healthy, not the bird's themselves - the article is too generic, did not cite the birds or any analysis of the poop which, etc. The fish available for food, healthy reefs and other parts of the ecosystem are the prize, not the actual bird poop. If the surrounding reefs did not have food to feed the birds and was not already nutrient rich, then none of this would matter. This is like saying that cow pies are the reason that pasture grass grows so well, instead of the nutrient rich soil that grows the grass for the cows to eat to make the pies.
This is a good reminder not to always trust or believe what you hear or read when it comes to the hobby. Most BRS videos are to sell products and are rarely completely accurate or offer any nuance to help people reef. Most reefers use data and studies like a drunk uses a lamppost... for support rather than illumination (Andrew Lang). The whole Vibrant thing from BRS should make people shudder about online videos and help. BRS was a huge proponent of dry rock for "no pests" yet dry rock grows the worst pests of all.
Please try and avoid any quick-action type of things when dealing with your algae. The unintended and long-term consequences are not often discussed in articles, videos or online, but can be devastating. No pesticides or magic in a bottle - just be smart, get some consumers and go slow. If you want to rehome your corals for a while, you can turn the lights off while your rocks develop things other than algae on them, but this does not work with coral, of course.
This article shows that low levels of urea can be used by some corals, but in levels more commensurate with what is already on the reef. Urea is preferred to nitrate since it is easier to convert to ammonium for the zoox to use. This study seems to contradict with the more generic seabird study is saying but also backed up the science that nitrate is of no use to zoox with the host spending MUCH energy to convert no3 back to nh[3,4].
https://www.sciencedirect.com/science/article/abs/pii/S0022098105005538
I know that I typed a lot, but just want to impress not to cut back on feeding the fish since the ammonia/ammonium from the fish waste is the only thing that for sure the corals can use for nitrogen... so don't think that the corals have enough "food" if you have no3 in the tank. The bottom line is that you have to keep importing food into your tank, but up the export of residual no3 and po4 and also get consumers for the algae.