This made me wonder if there might be any chance of hopping about a freighter from Mangalia, Romania to South Korea (I assume Busan)... Or at least whether Korean freight shipping lines are known to take passengers at least occasionally.

Korean ship docked at the Mangalia/2 Mai shipyard in Romania. Photo by the OP (hippietrail).
Has anyone here got any freighter travel experience? Where might I even check? Do people that travel this way enquire directly at shipyards or is it all done through agents etc?