Here's food for thought:
That algae in your tank thrives when conditions are right. Your coral and such need the light, so you have to leave that condition alone (unless your bulbs are OLD, then they can change freq. and put out light the algae likes, but corals don't necessarily like).
They also need food. That usually being phosphates and nitrates.
Nitrates you say are 0, and that's good.
Which leaves phosphates. You could test your phosphates, but they'd probably be 0, because the algae is eating them all. This is why i said testing for phosphates is kind of wothless, UNLESS you're testing the water you put in the tank before it gets there. That is an interesting tell.
So, here's the thing: Your tank has this food (phosphates) in it. Your algae is eating it, but not producing it.
If you cut off the source of the phosphates, your algae is going to just eat as much as it can and then start to die for lack of it.
So, if you replace your water with the same water you've been using, you're replenishing the algae's food, which is something you DON'T want to do. If your normal params are fine, just don't do any water changes for a bit, till you get to the good water, or you're just 'supercharging' that algae.
Now, lets say you do change your water, and start putting in new water with no phosphates/nitrates/whatever for the algae, now the algae in there already is still eating that food which is now not replenishing.
So, if you leave it in there, theoretically, it should eat up that food faster, because there'd be more of it.
Of course, you don't want it to overshadow your corals and cause them to die, but you get what I'm saying.
Cut them off at the supply chain, and you're ahead of the game.
Hope that helps. I mean, you saw my pictures, and mine's coming along...and if it can bounce back from that...so can you!