Is the Prospero Eel a quest fish or a normal fish to catch? If it is a quest fish then it won't show up in your Fishing Log. Also, if you finish the quest you won't be able to catch it again. Another example would be the Calico Trout found in Il Mheg in Longmirror Lake. The trout is a quest fish. Perhaps the eel is the same? And to confirm, I too, have finished the Crystalline Mean quests.