Adamwheel your are certain to reintroduce the dinos with your current livestock.
If you are lucky they might not thrive in the new one, but there seems to be a trend in getting dinos again after restart.
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Raidendex. I'd say you definately have dinos, not diatoms. (Dinos have a hard outer shell).
I'm sure it's not Ostreopsis. Perhaps it's Prorocentrum or something else.
Do take a look at pants site.
http://www.algaeid.com/identification/