Large amounts of algae in a system will be actively consuming the nitrates/phosphates in the water column. You won't be able to get an actually reliable reading.
One 50% water change won't solve parameter issues. If you have nitrate levels of 100, a 50% water change will drop that to 50, and then they will begin to rise from there.
Algae problems are a long, drawn out, frustrating battle. You will need to continue with manual removal of the problem algae during these large water changes.
I normally don't advocate the addition of livestock to a system to solve issues. It not only adds another eating/pooping creature to the system, which will help nitrates rise, but you also have to continue feeding it once all of the problem they are addressing is gone. But in a 125 gallon system, I might ask if there are plans on adding any tangs to the setup? They won't go after long hair algae that is overwhelming things, but when addressed can keep a well maintained lawn. I also like to have an urchin in my systems now after years of algae problems from only being able to use distilled water. Some food for thought.
