Most algae needs NO3 and PO4 to grow - at least small amounts of it. The anoxic bacteria in the sandbed can usually take care of nitrate, so I am not shocked that nitrates are very low, even with high PO4.
There is no real mystery to this. Just start swapping out your current sand with some new aragonite. Don't do too much at once. Don't feel like you have to get it all. The area in front and around the rock work is enough. Throttle your flow pumps back since new sand takes a while to "settle down." This is also a good time to change habits or introduce new equipment to make the new aragonite last longer... although you can just go back to doing what you did and just replace sand a bit sooner the next time.
The aragonite can also bond some metals, but if you use a high quality salt and fish food, then this is less of an issue IMO.
BTW - new tank syndrome can start to happen a lot sooner for people that use silica sand since silica won't bond to much, but does a good job of housing oxic and anoxic bacteria.
IMO, macro algae blooms coincide with water changes, or supplements, that replace likely-depleted iron in the system. Iron is very hard to keep up with very much macro at all.