Dosing nitrates and phosphates is arguably safer because at least you have a test kit that can tell you when you've gone too far.
Yes, dosing food would probably help, but there may be some question of the corals can access those particles....it will only help if it gets eaten.
As long as you have patience to make small additions that will seem "too small" and wait for results that may seem to take "too long" then you really won't have problems in any of those avenues.
Feeding your fish more is also an option....but not sure how far you're already pushing that envelope.
Generally, there's always room to add some NO3 (maybe the safest compound we dose....seems impossible to overdose) and PO4 to make up for shortfalls....and it's easy to dose small, controlled amounts. (I haven't had to dose PO4 persoanlly...yet.)