Any way you can have your water tested for nitrates and phosphates by a different test kit, maybe from another reefer or LFS? I'm wondering why you are battling HA if you have 0 nitrates and phosphates -- maybe you are overfeeding, but then you should at least detect some phosphates.
I use LaMotte to test my Nitrates and the Hanna Checker for phosphates.
IME testing phos with ANY signs of macro-algae's has been essentially pointless- the algae sucks them up before they reach detectable levels unless levels are extremely high. So yea, I'm sure there's some nutrients in tank, but as I don't feed often/much, I don't believe the nutrients are the biggest factor for the HA- more that I just haven't been able to eliminate it so they get enough to survive. With it being a small tank, never had had a large CUC going on, and no tangs to keep it nibbled at either.
I've tested 'trates using two different salifert kits, a red sea kit, and had a buddy at a chemical lab test it- all showed same readings of zero's, after which point I gave up trying to get a reading on it and just go by general appearance these days for the nutrient levels.