Bleeding fish is easiest done by cutting behind the gill plate.
That's what I was just going to say. Cut the main artery behind both sides of the gill plate and the fish will bleed out quickly. Just like pulmonary arteries on humans, all the blood has to go to the gills to oxygenate.
I've seen some nasty parasites outside the stomach wall - little yellowish maggot-like thingys....sometimes you wished you did not zoonose around in there