I don't think any clean-up crew would be able to compete with the growth rate of Dinoflagellates. You may notice that in the mornings, before lights on, the Dino. population is rather low, but after only a few minutes it is back at full throttle.
I recently beat a Dinoflagellates battle in my reef aquarium, and the method I used was that recommended by brandon429. That is Hydrogen Peroxide dosing. Hydrogen Peroxide has a really bad rep. but it really isn't as bad as made out. I found that dosing even over 10X the recommended "safe" dosage doesn't cause any visible harm, but I am obviously not going to ever recommend starting at 10 times the safe dose. The method I used was to black out the aquarium with black bags for 3 days and dose H2O2 to the aquarium, the use of a UV sterilizer correctly sized will also greatly help. I also would like to recommend that if your parameters check out, that you stop water changes until you are sure that the Dinoflagellates are kicked right back under control. Some trace elements in fresh saltwater fuel Dinoflagellate growth