"Not-Noun"s: Neologism or not?
Solution 1:
The OED has examples going back to the late 16th century, both with hyphen and as two separate words (the examples I give here are with the hyphen). It seems to have been common in situations where we might use the prefix "non-" or other methods of negation: "For not-payment of ministeris stipendis." (1590) "The eater despised the not-eater; and the not-eater iudged the eater." (1622) "If both the Beheaded and the Not-worshippers of the Beast were of the same kind." (1680)
There aren't many 18th century examples, but we also find the Victorians at it: "What He attributes to idols, i.e. not-gods." (1860) "A complete idea of a closed figure, and of the boundary which incloses it—the outline separating object from not-object." (1867)
It's hard to be certain whether the OED's examples reflect genuine patterns of usage, but they also have several from the 1990s which might indicate a new burst of popularity (as well as changing patterns of how they collect usage examples): "It would differ from..matter because of its immobility. It would be almost a not-being." (1995) "If he's including himself among the not-movers and not-shakers, socially unconscious, and poorly educated, why should anyone vote for him?" (Usenet, 1992)
You might surmise an increased popularity of "not" since the 1990s is connected with the film ''Wayne's World'' (which popularised "not" as a stand-alone negation) or computing, both of which the OED mentions. But it is an old way of forming a negative, which has persisted on and off for over 400 years.
Reference: "not, adv., n., and int." OED Online. Oxford University Press, June 2021. Web. 23 August 2021.
Solution 2:
Dropping the 'technical' as being ill-defined, 'Is this acceptable?' (correct morphology) is hard enough to address.
'It has been done for certain words in the past' does not guarantee that there is a universally productive rule. And neither does increased employment by SF writers and film-makers (and logicians).
As always, clarity is paramount. In a superb scene from 'Sherlock', Molly Hooper begged of Mycroft "How did Sherlock recognise [the body of a young woman on the slab] from ... not her face?"
Less transparent, but still reasonably clear,'Not the Nine O'Clock News', a British television sketch comedy show, was broadcast on BBC2 from 1979 to 1982 for those wishing for an alternative to what was probably BBC's flagship programme at the time.
At a maths education development meeting I once attended, someone gave voice to a common concern that too many SMP GCSE investigations involved the triangle numbers. He continued "We're trying for one involving the set {2, 4, 5, 7, 8, 9, 11, 12, 13, 14, 16 ...} – 'not the triangle numbers'."
But as always with negation, scope for ambiguity will arise with some examples. When the inimitablt Richard (DI Poole) (Ben Miller) was replaced as the lead in 'Death in Paradise', I'm afraid I didn't assimilate his replacement's name (Humphrey) for years (I stopped watching), so on the odd occasion my wife mentioned the character I used 'not Richard'. And the next replacement was 'not not Richard' (until I discovered Jack Mooney was very entertaining). But this would obviously be unacceptable in general conversation.
So the answer on acceptability has to be: reasonable if used with care, in fact often quirky / witty. I'd add: probably better avoided in formal contexts.
Stuart has probably given the best shot at earliest use (though an accurate date will be impossible to find). I'm unaware of aprecise term; litotes requires irony, which is obviously not always the case here: 'not-payment' is unmarked for irony.