Hello...

[Winters]

Beneficial algae, like chaeto, is a very hardy competitor for these nutrients and can draw down the levels for unwanted varieties, and then the nitrates can be directly exported by pruning the stuff out.

I agree!

When I started my tank an year+ ago, it went through several algal blooms. (I'm using well water filtered through RO/DI) Hair algae was definitely a big problem. I tried the usual suspects: urchins, Sea Hare, Lettuce Nudibranchs,
snails, Hermit Crabs, Emerald Crabs, Lawnmower Blennies, etc. and nothing worked. I kept having to take rock out and scrub the horrid hair algae off every other month.

UNTIL.. I got a clump of Chaetomorpha, and a light for the sump. I put it into the sump and did one last algae cleaning. I've never had to clean it again. In fact, I don't have a single strand of hair algae anywhere in my 90g any more. Best $10 I've ever spent.

I believe the issue, as you've been suggested, is Phosphates and Nitrates, which the macroalgae should help remove. (And even if your test kit doesn't seem to show much of it present there could still be enough in there to cause a problem, but since it's all being absorbed by the hair algae the test may not be detecting it) I would definitely try Chaeto before going the Phosban (and other chemicals, etc.) route. Cheaper, natural, and considerably easier.

Good luck!