How long have you had this issue- and how new is your tank? Maybe share your ICP test results as well Dinos are just one of those things that will go away after some time.
Dinoflagellates do tend however to emerge following extended periods of zero or near-zero phosphates and nitrates.
ICP usually brings more questions than answers. If you know what it does and what to expect, it might be of some use. For compounds like no3 and po4, they are doing color changing test kits since the plasma interface cannot detect compounds.
Dinos are mostly a product of sterile, fresh places to take hold. If you don't have any corals yet, then keep the lights off and let some film bacteria and stuff coat the dead/dry rock (assuming) so that there are less places for the dinos to colonize.