I find that dosing either an N source or P source, depending on which is limited, tends to pull down the other one when I am carbon dosing. I assume that will happen to some extend now that you are not carbon dosing.
When boosting phosphate I find the tank actually looks great when I overshoot my target, my corals seem to love it higher after it’s been too low; however, I get hair algae when I let phosphate linger at the higher levels. Getting the hair algae to go away in my tank takes much longer than it does to appear, so I don’t let my phosphate stay at higher levels. I usually try to bring back down to target within a week.
Once I get phosphate up, bringing it back down and easier and more predictable. I can get it to decline and monitor the trend as apposed to be stuck at zero when trying to raise it.