Truth be told, I'd worry more about raising the nitrates and not worry about the phosphates just yet. In my own tank, I had the same situation and was chasing the same problem. The tank also got a case of ugly real quick too, with brown crud all over the place which was likely diatoms.
You need to have both in the tank for a proper balance.
Once all the nitrates are exported and consumed, things stop growing, and then also stop consuming phosphates. Your SPS likely aren't responding poorly to excess phosphates, they're responding poorly to insufficient nitrates. Once you get your nitrate levels up your livestock will start consuming more nutrients and thus consuming more phosphates as well. This leaves a window for things like diatoms, which are primarily phosphate consumers, to thrive.
I struggled with this for a LONG time when I was running biopellets. They're just so good at reducing nitrates that I ended up with a huge nitrate deficiency and spiking phosphates. Once I took out the pellets and increased my nitrate levels the tank really started to take off. Phosphates dropped once other higher lifeforms began to thrive and the diatoms died off.
Do you have a turf scrubber or refugium with chaeto going? I always recommend people start a 'build thread' to chronicle their tank, as it lets us get a bigger picture of the whole system.