I beat a nasty case of dinos and have been dino free for around a year. I dosed Si to help create diatom blooms. The reason this helps is because they produce polyunsaturated aldehydes or PUAs. PUA is toxic to dinos and helps to suppress the bloom. However the thing that really beat them back was keeping PO4 at 0.1 ppm min and NO3 at 5 ppm min and manual removal as needed. Took about 6 months, again my case was REALLY BAD, but they haven't come back.
Randy wrote an article about Si in sea water and its benefits for the aquarium. The Si itself doesn't help with dinos, just the PUAs from the resulting diatom bloom. Si is also used by snails so should help their long term survival and health theoretically. You can continue to dose but ot probably won't do any good once you get past 2 ppm. The only Si tester I found that is worth while is the Hanna one.