Just an update! After three windows (including one 44 hour wait for one of them), I finally managed to snag a Helicoprion! HQ at that! With it being the last fish I needed for Feast of Famine, I was finally able to turn in the quest and get my DEFINITELY earned new title.

Here's hoping they add a new legends quest in Stormblood! And hopefully not one with such stupid and stringent catch requirements.