u'd be surprised at how fast nutrient are absorbed - especially by these simple organisms like dino and bacteria - that's why they explode so quickly. looks like your tank has a decent bioload that's constantly producing nutrient (fish and invert poop). I think what's happened to your tank is this: before the dinos - the tank probably has reached an equilibrium between rate of nutrient production vs the rate of nutrient removal of which your GHA was a big part. After this weekend when you got rid of GHA, its likely that it left a sudden nutrient removal vacuum that was big enough to tip the scale. Dinos, being a very fast and efficient nutrient absorber, quickly exploded and filled up the void left by the removal of gha.
So, assuming your nutrient production rate stays the same (not sure you will want to starve your fish to make them poop less), the issue your tank has isn't that your have "too low nutrient", it's that your "nutrient absorption" capacity has been temporarily reduced and Dino's picking up the slack. To fix, you will need to reintroduce additional other nutrient absorption capacity - the more the merrier - of any non-dino type (bacteria, refugium/chaeto, more skimming, even filter socks) while at the same time remove dinos to recreate that vacuum to force these other players to pick up the slack. It's often difficult b/c these other players don't absorb nutrient as fast as dinos that's why battling dinos is harder and takes time. Adding nitrate adds nutrient that ALL the "absorbers" need, so it really boils down to a math game of what currently has a bigger "absorption capacity" between dinos and everything else and will require constant manual removal of the dinos to reduce its "absorption capacity" while waiting for the nitrate to feed and increase the biomass of everything else so that eventually they will be able to outcompete.
This is the general direction for combatting dinos so if whatever you do is inline with this general direction it will work with enough time and persistence. Bacteria and phyto should both help if they are live. If dead then they will just rot and add to the nutrient load. Also the more variety the better b/c the nutrient isn't just 1 thing - its poop, dissolved organics, amino acids, rotting biomass, ammonia, nitrite, nitrate, etc.. although most will eventually break down into No3/Po4, different organism prefer to target different pieces of this pie that's why "biodiversity" is the name of the game for nutrient control.