I do not agree there is zero nitrates based on details in the post
Its just a test reading, our threads are full of mis reads. Post pic of reading and comparison test,taken when the water is dirtiest just before a water change. The lfs will usually test, have them use a kit other than the API kit you may be using.
Unless a second kit can be shown to verify zero nitrates compared to the API nitrate test original we would work from the assumption the algae is enjoying the excess nitrate from overstocked fish loading, all heavy feeders and waste producers, and the system is eutrophic
The plants didnt use up the nitrate nor the algae, there's some there.
We look for pocketed organic reserves, any type of clogged sandbed etc
The right move is a total tank clean down in such a way as to prevent recycling and reduction of the fish bioload, thats specifically what lessens water change work and nothing else. Adding filters, catch basins for waste, won't...it needs to be reduction in biomass until you can be home to change water
Diluting with extra tanks helps, if you can't expand then downsize fish and clean that tank free of organics. Its like a plaque ridden mouth, tons of anaerobic pocketing and increased biological oxygen demand, favors pathogenic growth all kinds of reason to clean out a eutrophic tank and take forced control. Each large algae eating fish was actually setting the stage for future problems. Time to clean the entire sandbed and system 100%, done right it doesn't hurt your filtration one bit Ive done it twenty times
I don't agree that much free phosphate would be left unbound while the nitrate is left to zero, the demand is opposite.
Something needed to change anyway, the enjoyment factor of the tank wasnt at an all time high with sheets of algae
If we watch post trends, you see comparison threads where various test kits give wild reading variances, don't accept one off API posts as any kind of accurate reading, go off biology. Biology says you may have a nutrient sink in the presence of high organic sludge decomposition and its time to flush out all that waste to get control of things