i have a hanna colorimeter to test the po4. you (and anyone else) can borrow it anytime you want. though it was crazy expensive and the reagents aren't cheap either so i gotta ask $1 per test. i would say people could bring water samples, but i would be afraid that whatever you bring the water over in could contaminate the sample.
i personally think you can have algae even with 'prefect' water, so don't go too crazy on water changes till we get some numbers on the water (it would have to be really bad and your makeup water really good for it to matter imo, otherwise you could just be feeding the algae with fresh micro-nutrients). if there are enough nutrients for corals/coralline to live then there are enough nutrients for algae to live, it's just a matter of having enough happy 'good' stuff in the tank to outcompete the 'bad' stuff. remember that nutrients in water are constantly being generated and consumed, so don't think of it as 'my nitrates are 20' think of it as 'my tank is consuming/exporting less nitrate than it's producing, giving me a right-now-snapshot equilibrium of 20 nitrate'.
so, my theory is that you need to get the hair algae out as best you can, either by hand/scrubbing or by a critter. queen conchs are really good on most hair algae. then without the mass of aglae sucking down what it wants, dominating the system and keeping everything else in the tank suppressed and from being able to compete, those nutrients (and by nutrient i mean the whole range, not just the 'bad' things we test for like nitrate/phosphate,...) will then be available to the other good stuff (corals, clams, macro,...) and then with a little time they can take charge and become dominant and suck down nutrients faster than the hair algae and outcompete it. it's really cool when you hit that breakpoint, all the algae in your tank just dissapears practically overnight.