The Silica may not help with the Prorocentrum, but dosing it should benefit other organisms, which might help with balancing overall (or it might doing nothing)!? If you dose too much, you'll probably see more diatoms, which can look a bit like dinos. They'll look drastically different than dinos under the microscope. I dose it in my tanks habitually.
I think the recommendation is total black out, but what I've done in the past, which worked for me, was simply turning the lights off for a few days, then I turn the blues on, give it a couple days, followed by the whites. I don't cover the tank, but there's no direct light, only ambient room light.
The above worked for Ostreopsis for me. I believe Prorocentrum is more stubborn, but you could try it for a couple days, see if it makes a difference. If not, try blocking all light.
I would take a turkey baster and blast the rocks and sand at night to get them in the water. I ran carbon passively during this time frame. I don't know if it helped or not, but I ran it, so I wanted to add it here.
Finally, manual removal of what you see probably wouldn't hurt, especially if you have a lot.