You named the problem.....N:0 and P:near-zero assures that nothing but brutal survivors like cyano and dino's will proliferate.
Cyano can make it's own nitrogen and carbon and has exceptional abilities to use phosphorus sources. Dino's eat...everything. All the good guys that you'd want to be happy and growing (corals, green algae, etc) require some dissolved nutrients.
If dino's have recently bloomed or are presently bloomed I would raise N and P "directly" by using fertilizers like Seachem Flourish or Brightwell's Neo line. DIY is a good option too. Target ≥0.10 ppm for PO4 and ≥5-10 ppm for NO3.
Not everyone gets dino blooms – there's a pattern at work if it's that predictable.
Common misconception.
@BoomCorals and
@PAXpress check out at least the first post of
Dinoflagellates – Are You Tired Of Battling Altogether?.