I would get an ICP-Test (preferably ICP-MS over ICP-OES).
It can be difficult to figure out why dinoflagellates take over a tank. Sometimes it appears to be a single parameter that is off which keeps other organisms from establishing that would outcompete the dinoflagellates otherwise.
If you have detectable nutrient levels during an outbreak of
any sort, you have to take into account that all that growth requires nutrients. This means your actual nutrient levels are much higher than they seem.
Dinoflagellate blooms can actually consume quite a lot of nutrients. I know people often associate dinoflagellates with too low nutrient levels, but that doesn't necessarily applies to all tanks. Its pretty easy to get nutrients back up if this causes any trouble.
The microscopy images are quite blurry, but you might be able to identify the dinoflagellates by their movement. If a cell is appearing to cycle a point instead of moving all over the place in straight lines it is probably Ostreopsis (or Coolia, but those are quite rare). Prorocentrum and Amphidinium move straight forward and do not cycle a fixed point. Other dinoflagellate genera appear to be rare, as well in reef tanks or look too similar to be distinguished from the other commonly known ones. If you can get better images, you can compare them to images from my
microscopy thread or the
dinoflagellate identification guide.
Regarding silicate dosing: It can work, but it doesn't have to. Down below you can see Ostreopsis sp. surrounded by Diatoms, but still absolutely thriving. The thing is: Dinoflagellates can prey on diatoms which means you really have to have A LOT of diatoms to suffocate Dinoflagellate growth. Sometimes it just doesn't work. However, I didn't see any diatoms in your photos... Maybe your SiO₂/SiO₄ levels are still too low? The ICP-Test will tell us if you need to add more silicate.