Wellthe phosphate is likely less harmful to fish than the chemicals :/ I would say invest in some plants like duckweed, so there is something to out compete the algae and you can throw it out when there are too many, permanantly removing the algae.
Other low light fast growing plants might be a good choice too. I thought brown algae generally manifests in low light?
I have anubias, cryptocoryne wendtii, java fern and bolbitis heteroclita.
My tank has 7600k LED lighting, I believe that would be considered low lighting. I've been leaving the light on for about 10 hours.
I would prefer to not use chemicals but I have yet to find an alternative solution.