Forget test kits for a minute. No matter what your test kit reads, no matter how high or how low your nutrient level is, algae could still grow or not grow. Why? I have no idea. I am sure Randy does, but I certainly don't, except what I already proposed and if eliminating nutrients were all it was. That is simple, dump out your tank and start a new one with new water and rocks and see what happens. ;)
It's like quarantining, if that would keep your fish safe, then why are there hundreds of posts saying OMG, I quarantined for 3 years and 2 months and all my fish have ich. You know I am right. Yeah you do.
This stuff is so easy but we feel the need to make it difficult. You can't go to school for this or you will be so confused you will not know what to think because a living tank is too complicated and we can't test for bacteria, viruses, types of algae, light, temperature, phases of the moon (no, really) and micronutrients that we acquire through rocks, LFSs, corals and excretions of fish. There are to many variables and if it were easy, there would be no problems.