Your tectonics are fine, groovey, I say stop worrying with them

As for your question: cold currents tend to be deeper and narrower, so they normally follow the continental shelves. Warmer currents, on the other hand, are shallow and tend to spread out - which means, you can take more liberty with the warm currents than with the cold ones.

Those basins are great, both for history/civilization as for climate stabilization. They will probably generate their own closed currents. (google "black sea currents" and look at the images results).