if you have nitrates and phos in your tank the coral will get to it. HOwever, they do not process it directly , and the speed is much slower than absorptioin by the algaes.
In nature, there will always be algae to help control and cycle nutrients .
Yes, change water, make sure you use water with no nutrients. Cleanup crew is fine, but make sure they have food to eat, because after you have no algae, the cleanup crew may die, thus reintroducing nutrients and starting algae bloom again.
i would decrease white daylight inside my display area, to maybe 3 to 5 hours per day, and use mainly actinic or blue lights for maybe 7 to 10 hours. per day.
When I scuba, i notice that most colors from white spectrum is already getting filtered out at 10 feet, and by the time i get to bottom where most corals and livestock is at, it is mainly blue colors.
exception to this is acroporas and montis that are near surface and require higher stronger light. Place those higher up and in center of your tank. But i think 4 to 6 hours is already plenty as the sun directly shines on them maybe that long.
this will slightly decrease growlth of algae in your display area.
increase bright daylight in your refugium, if you have one, so the algae grows strongly there, .