Etymology of "slang"
Solution 1:
I found nothing to add to or subtract from Liberman's analysis of others' etymology of 'slang'. That nothing was to be expected. As made clear by Liberman's reference to a note from John Sampson that is not readily available to me, the resources he could bring to bear on the question exceeded mine. This 'answer', then, must present only ephemera of passing interest to me, and possibly others.
No dispute over Liberman's etymology of 'slang' is possible. As he states outright, the etymology is not his. So, it is easy to understand Liberman's frustration, as expressed in his 2016 OUPblog article "The origin of the word 'slang' is known!":
On several websites I now find mentions of the etymology ascribed to me (though I am not its discoverer), but they are brief and noncommittal. At this rate of going, we’ll never make progress. Inspired by the belief that the explanation I defend is not just one of many to be considered but the true one, I decided to return to the question that no longer interests me but may interest some other people. And I’d like to ask: "Why are people so cautious? Why do they hedge instead of celebrating a small victory?" Perhaps because sitting on the fence (or on the hedge, or wherever) is safe, while defending an opinion that has not yet become common property is risky. I would not have fought with such vigor for my own conclusion, but it is not mine, and I feel obliged to break a lance for those who can no longer do so themselves.
For my part, I find Liberman's analysis of the etymology of 'slang' convincing...until and unless a better explanation comes along. However, I disagree with his conjectures about why people are "so cautious". My own "hedge" ("until and unless") is motivated by nothing more than a refusal to firmly and finally conclude any thing whatsoever while a bit of mystery remains; that is, until all the evidence is in and can be examined by me, I'm happy with the etymology recapped by Liberman.
Green's summary dismissal of the evidence as not "concrete", as not "hard evidence" supporting the existing etymology, does contain what he considers the substance of the "relevant note by John Sampson" mentioned by Liberman:
[John Sampson's article] stresses the absence of any links to Romani, while noting the importance of a slang or strip of land....
Among others, notably Hotten (A Dictionary of Modern Slang, Cant, and Vulgar Words, 1860; The Slang Dictionary, 1865), one early secondary source, Barrere and Leland, does ascribe some senses of 'slang' to a "gypsy origin" (see A dictionary of slang, jargon & cant, 1889-90), yet Sampson, an acknowledged expert on gypsy dialect, later contradicted that origin. Barrere and Leland as well as Hotten, however, did contribute a substantial number of the facts later woven together, along with Sampson's denial of a gypsy origin, by Liberman; other facts were contributed by Joseph Wright in his English Dialect Dictionary (1898-1905).
Overall, Liberman's reasoning is easy to follow, and comprehensive. He deserves credit for bringing together the existing evidence and weaving it into a cohesive, logical account of the etymology of slang. That the account has not been more widely accepted rightly merits mild censure.
As always, I exhausted the primary sources available to me before presuming to agree or disagree with the existing origin stories. While largely unproductive, my search did turn up some uses the sense of which remains opaque. For example, the earliest use I found (1724) with reference to a type of language (poetical), did not have sufficient context for me to take the sense with any certainty:
What I have now said on the Topics of Logic and Rhetoric is meant, I own, with a View to what I hope to say hereafter concerning Poetry, properly so call'd. Fain would I, methinks, if possible, retrieve in some measure that Divine Faculty from the stupid Indifferency and Neglect it languishes under in this Age; and get it at least a little of the Esteem it has always before possess'd, in Ages and Countries where Vertue and good Taste have obtained. This were the means, indeed to recommend whatever is Great and Good most powerfully. And if this Attempt of mine could but have any Success; and could but revive, in the polite World, the pure and chaste Spirit of this Gift, instead of the Trade and Slango of it, I should have my End; and feel an inward Pride in helping to raise to its intrinsic Value, in Men's Estimation, an Art, which the Ignorance and Folly, both of many who have pretended to it, and of Others around them, have sunk so very low.
Caledonian Mercury, 06 October 1724 (paywalled)
My best interpretation of "Slango" is something like '[poetry's appeal to] the common taste for vulgar dash, that is, sustained rhythmic jingo ['jingo' in the sense of a "conjuror's call for the appearance of something" (OED)]'.
The uses of 'slang' that I found from before 1724 (having restricted my search to the 18th century) appeared to be uses as the preterite of 'sling', that is, to "move with some force or speed; to fly as if thrown by a sling" (OED) or to "advance, walk, etc., with long or swinging strides" (OED) in the 1703 citation, and the obvious to "throw or cast (stones, etc.) by means of a sling" (OED) in the 1718 citation:
...but know thou, the Emperor was aided by the nearest kinsman he and you have, wherewith she slang away so swiftly, that she seemed to outstrip the wind, and suddenly vanished out of sight.
The Honour of Chivalry, Jerónimo Fernández, 1703
At this Hejage stuck the corner of his Vest into his Girdle, and putting one of the Stones into it that they used to throw out of the Engines, slang it; his Example set them on Work afresh.
The History of the Saracens, Simon Ockley, 1718
After 1724, but prior to the 1756 OED attestation (which they note may refer to "customs or habits rather than language"), I find 'slang' in the sense of "a long narrow strip of land" (OED),
...accessible only by a narrow Slang of Earth which rises like a Causeway in the middle of the Water....
The General History of China, J.-B. Du Halde, 1739
as the preterite of 'sling' in the sense of "throw or cast [with] a sling" in a life of King David (1740), and a use in a letter dated 1595 but published in 1746, the sense of which I have not as yet deciphered, but which seems unlikely to have any connection with the general sense of 'a type of language':
My Lord Monjoy was here, and spake with the Queen in privat, having his Gown girt about hym, because of an Ague: Some say he would faine be a Cownsailor. And I hard that 200 should in privat say to another, whom he trusted much, that the Long Slang, meaning 1000 [Earl of Essex] since d d going away, was never from 1500; and that . . . . now wold doe nothing but what he and my Lord knew.
Letters and Memorials of State
Solution 2:
I am not certain myself, but it is probably derived from the pretiet sense of the word sling, which was slang. This possible origin is hinted at in your own research, which notes the similarity found in the work of John Ogilvie and Noah Webster, but you seem to have dismissed this possibility since you have not included it in your research. Perhaps you should reconsider that.
It is also what Eric Partridge himself proposes as the probable origin in my personal copy of A Short Etymological Dictionary of the English Language:
slang, slangy. See SLING para. 2.
Sling … 2. Perh from 'to sling'—prob from the dial pp slang—and there for elliptical for 'slang , i.e. slung, language', is in the n *slang, orig the language of the underworld, now merely the unconventional (non-dial) speech of all casses: cf the sl 'sling off at' to cheek, to abuse, and Nor slengja kjeften, to use slang (lit, to sling the jaw), and slengjeord. (See esp P and P1 at slang.)
The Century Dictionary and Cyclopedia (C.D.C.), which represents something of an unapproved continuation of Ogville and Webster's work also proposes sling as the probable origin.
[Of obscure cant origin; the form suggests a connection with sling, in a way indicated by the use of sling and fling in 'to sling epithets,''to *fling reproaches,' etc., and by similar uses of related Scand. forms, as Norw. sleng, a slinging, a device, a burden of a song; slengja, sling (slengja kjefte, abuse, lit. 'sling the jaw'; slengjenamn, a nickname; slengje-ord, an insulting word or allusion; icel. slyngr, slyngum, cunning. See sling1 The noun in this view, must have arisen in quasi composition (slang-patter, slang-word, slang-name, ect., or else from the verb. Evidence of early use is lacking. The word has nothing to do with language or lingo, and there is no evidence to establish a Gipsy origin.]
Google ngrams does not seem to support the proposed quasi-compositions, since the earliest those go back on their charts is just shortly after 1800, so it probably arose from the verb itself.
Granted, these references do not seem too terribly convinced of their propositions, but there is a reason I suspect this is the case beyond mere reference: When you consider what slang is, which is essentially inappropriate use of language*, it makes a great deal of sense figuratively speaking, because it is largely considered to be inappropriate language, and hence careless or reckless in nature.
We have phrases in English such as shoot one's mouth off which seems very similar to the Norweigen slengja kjeften, which very easily suggests we might have adopted the word from there.
We also have throw around which suggest the careless use of words, and I must admit that throwing is one of the more reckless or careless actions somebody can do. You are very likely to break something by throwing it, without deliberate aim it could end up anywhere and even if you do aim to hit a particular mark, you can miss it entirely.
It also contrasts quite well with the much more deliberate and careful placement of words we often seek to aid people with here at E.L.U., which can be found in Shakespeare's King Henry the Sixth:
These are the city gates, the gates of Rouen,
Through which our policy must make a breach:
Take heed, be wary how you place your words;
Talk like the vulgar sort of market men
That come to gather money for their corn.
The C.D.C. also suggests that one of the earliest 19th century definitions of the word is in Walter Scott's Redgauntlet, which predates even Webster's magnum opus by four years. Although the word is older than that, the C.D.C. takes this as evidence that the word was still relatively rare, and the actual quotation used may also fit in well with the metaphoric slinging:
This he soon found was to no purpose; for what did actually reach his ears was disguised so completely by the use of cant words, and the thieves'-Latin called slang, that even when he caught the words, he found himself as far as ever from the sense of their conversation.
It makes sense that the words would be hard to catch and understand if the thieves were slinging them around. Similarly, the person who knew slang well in your proposed earliest attestation is named Thomas Throw, which makes for quite a good joke if this hypothesis is correct.
Granted, all of this could be mere coincidence, but basically, the point I have to make is that English speakers have a penchant for this sort of metaphor, which I think should be considered persuasive circumstantial evidence in the absence of antedating or strong scholarly consensus.
*A few dictionaries, most particularly older ones, will phrase this sentiment in different ways, but a recent reference can be found in Collins English Dictionary—Complete and Unabridged 12th edition.