The phyto has a greater density than the water its in. This means if you effectively amplify gravity through centripital force, you can turn your green water test-tube into a concentrated green goo chunk at the bottom of the test tube, with clear water on top. Then you pour off the clear water, add new water without fertilizers, stir, and you have cleaned up the plankton.
If you need a centrifuge, you can DIY them quite easily. When I was really into chem, I machined a dual test-tube holder deal that went into the chuck of a high speed drill. BALENCE BALENCE BALENCE! Balenceing the loads was absoultly crucial, and it ended up snapping the snout of the drill off when i got sloppy with the balenceing and had the drill pinched solid in a vice. I was only in 8th grade at the time, so my dad was pretty relaxed about breaking 2 lights and putting a hole through the wall... But seriously, there are pretty easy safe DIY plans to make a low G centrifuge.
However, I purposely does high nutrient water from my cichlid tank into my reefs.... So I would be the wrong guy to be telling you its important to clean the solution of excess firtilizers before adding.