....hmmmmmm
Well, again they've gone out of their way to take photographs that miss all of the systematic characters you need to make an informed identification.
The Gulf of Mexico beast - interesting. The scales are too small for it to be Lepidoteuthis, and it does look as if it had tentacles (the two narrow limbs, partially in shot); Lepidoteuthis by this stage (mantle length - even though no scale is provided it is obvious we are not looking at a paralarva) has only 8 arms (the tentacles would be several mm long, filamentous and not visible) ; so, Lepidoteuthis can be discounted.
We get Pholidoteuthis boschmai here in New Zealand waters; I've never seen an adult with tentacles (they are always lost/jettisoned/?autotomised at capture); but whatever it is it certainly is not this species. I've not ever seen P. adami (other than pics in books) - but if that is a colour photograph (I am having trouble - am quite colour blind; things look very brown/purply or black to me) then I doubt it is a Pholidoteuthis (the colour of which is very (indisputably) red for both P. adami and P. boschmai). The way the skin has abraded from the posterior portion of the mantle (the pointy end; where the skin goes from scaley and dark to smooth and white) is very Pholidoteuthis-like (I think there's something interesting in this area in live Pholidoteuthis that is lost during capture; either fantastically delicate skin, something glandular or something structural; I'd love to know what it was).
It could very easily be a species of Mastigoteuthis (including those referred to Echinoteuthis or Magnoteuthis); I've seen large things just like this before, this colour (if a colour pic) ... and in fact am describing one right now. I really need to see the 'tail' on the beast, a close-up pic of the sucker rings and a squiz at either the mantle- or funnel-locking cartilage to make an ident (in fact the locking cartilage would suffice to make an ident).
Re the other pic, I've seen one Thysanoteuthis rhombus only (bizarre, taken from 50°S - well outside of its recognised distribution). What struck me when I first looked at it was how similar it was to Sepioteuthis in overall facies. In fact Thysanoteuthis was first described as a Sepioteuthis, so we weren't the first to make that mistake. I'll either/or this myself right now (though the eye is a give away).
I think the other squid you refer to (the one with ribs down the fins) ... is that Chthenopteryx? Chthenopteryx is a very distinctive (and small) squid .... not a lot like this brute I'm afraid.
Disclaimer "everything written above could be total nonsense"
Cheers
O