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Eddie Howard, Marine Biologist at the Island Bay Marine Education Centre, who came across the giant squid carcass washed up on a remote Wellington beach over the weekend, gave me permission to share his FB album with the photos he took--you can view them here. Luckily for us he has a science/education background and did a great job documenting the find including taking some measurements!
Looking at the photos of the buccal region, with the beak missing, I think they are probably salivary glands that are hanging out now that the buccal bulb has been removed.
Eddie did manage to get a piece of tissue from the specimen so hopefully we can get a little more information about it--it will be A. dux but it would be interesting to look at the genetics of the specimens we've seen around NZ a little more closely!