I've battled both ostreopsis and gambierdiscus. I never found anything that could beat gambierdiscus (UV, low nutrients, Ultra Algae X, lights out, peroxide, diatom filtration, etc.). I had to break down the tank. Unfortunately, after restarting, I developed an ostreopsis bloom. As several others have reported, ostreopsis can be beaten by nutrients. Grow turf algae at all costs (not chaeto or macro algae - they were just hosting more dinos)! Why skim if you are just pouring it back in? I removed the skimmer all together and did my best to grow algae wherever I could. I made a simple upflow algae screen and later a down flow version. As algae starts to grow on the screen, dinos eventually disappear in the tank. I removed my skimmer last June and have been dino free since August.
I respectfully disagree. Ostreopsis cannot be beaten by nutrients reduction before killing your corals. My nutrient level is as low as 0,0, acroporas are really pale whitish starving to death and despite the aquarium sits in the sunlight I get no algae at all, neither on the glass walls or the botton. Nutrients are so low I can't run an ATS. Therefore I can't admit that they can be beaten with nutrient strip.
Anyhow, it's very interesting what you stated about the skimmer, I had a similar experience six weeks ago: I neglected one of my aquariums (no skimmer, no reactors, nothing but manual water replenishment) and it was the first to beat the ostreopsis bloom.