"I'm given to understand that the flesh of the Giant Squid reeks of ammonia.'
They may very well. I've fished for about 37 years on the outer banks of North Carolina, and one of the most prolific and tasty fish along the coast is the Croaker. I have caught many of them with red flesh in places that has a heavy iodine taste. I much prefer them without the medication.
Yikes! I don't know about Giant Squid, but we bought a lobster tail last year (to cook at home on New Year's Eve; our tradition) and it, too, just reeked of ammonia during baking. It was gawd-awful...one of the worst smells I've ever smelled. Yuck!
(We got our money back. I had to keep the thing out on the porch overnight as it was stinking up the entire house!)