A fourth theory, and its demise
The various sources I consulted seem to gravitate toward the first possibility outlined above, but other hypotheses have been suggested as well. One of the earliest suggestions is from Thomas Blount, Glossographia Anglicana Nova: Or, A Dictionary, Interpreting Such Hard Words of whatever Language, as are at present used in the English Tongue, with their Etymologies, Definitions, &c. (1707):
Quandary, (Fr. Qu'en diray-je, what shall I say to it) a Study or Doubt what to do.
This theory finds adherents as early as Elisha Coles, An English Dictionary, Explainging the Difficult Terms that are used in Divinity, Husbandry, Physick, Philosophy, Law, Navigation, Mathematicks, and other Arts and Sciences (1717), through many editions of Nathan Bailey, An Universal Etymological English Dictionary (e.g., the twenty-first edition, 1775), and at least as late as William Davidson & Joseph Alcock, English Grammar and Analysis (1889). The theory's Waterloo seems to have been the publication of Murray's OED volume 8 in 1902, which (according to a comment in Notes and Queries (October 25, 1902) "dismissed" the "qu-en dirai-je?" explanation.
Francis Grose, A Classical Dictionary of the Vulgar Tongue (1788) reports the French suggestion but also an Italian alternative:
QUANDARY. To be in a quandary; to be puzzled. Also one so over-gorged, as to be doubtful which he would do first, sh—e or spew. Some derive the term quandary from the French phrase qu'en diraije? what shall I say of it? others from an Italian word signifying a conjuror's circle.
'Quandary' and 'quandare'
Thomas Wright, A Dictionary of Obsolete and Provincial English, volume 2 (1857) notes that an early variant of quandary was quandare:
QUANDARE, s. A strait; a quandary.
But after that his father did more earnestly urge him, he brought him into a quandare, that indeed hee knew not whether he might better obey shame or love. Terence in English, 1641.
The relevance of quandare comes up in Notes and Queries, January 7, 1905) in an item by none other than Walter Skeat, the person responsible for the wandreth hypothesis back in the 1880s (in An Etymological Dictionary of the English Language) (1881, 1883, 1888, page 482). Skeat seems to have repented of his earlier etymological theory by 1905. In any case, here (at full length) is his comment in the January 7, 1905, issue of Notes and Queries:
"QUANDARY." — Many speculations have been hazarded as to the origin of this word; but we have all of us overlooked a highly important piece of evidence, to which Dr. Ellis drew attention as far back as 1871. The 'N.E.D.' gives the earlist quotation as from Lily's 'Euphues': "in a great quandarie," ed. Arber, p. 45, the date being 1579.
The next quotation is the very important one from Stanyhurst's 'Virgil' (ed. Arber, p. 94) in which quandáre is so used as to show that the accent was on the penultimate, the date being 1582.
The next quotation is dated 1611. But there is another notice of the word, in 1582, which practically explains its origin. This is from Rich. Mulcaster's 'First Part of the Elementarie which entreateth chefelie of the right writing of oue English tung,' printed at London, 1582.
In describing the sound of the letter e Mulcaster says:—
"Whensoeuer E is the last letter {in a word} and soundeth, it soundeth sharp, as mé, sé {see}, wé, agré {agree}: sauing in the, the article, ye the pronown, and in Latin words, or of a Latin form, when theie be vsed English-like, as certiorare {sic}, quandare, where e soundeth full and brode after the originall Latin."
That is to say, that an expert in English pronunciation, writing at the very time when the word was quite new, distinctly tells us that quandare is a word "of a Latin form," and that it is used "English-like," i.e., with some very slight change. Dr. Ellis remarks on this: "Observe that quandary is referred to a Latin origin, quam dare, as if they were the first words of a writ." See his 'English Pronunciation,' p. 912.
I much doubt if quam dare is right; it is difficult to see how a sentence can thus begin. But if anyone can produce an example, the question will be settled.
My own guess is that quan: dare is a playful mode of reference to the phrase quantum dare, "how much to give." This is a question which causes perplexity every day, notably to one who contemplates going to law, or contributing a subscription, or buying any luxury or even any necessity. At every turn this searching question puts the thinker "in a quandary." For such an abbreviation, compare verbum sap., infra dig., pro tem., nem. con., &c.
Skeat thus appears not only to have abandoned the wandreth hypothesis but to have embraced the quasi-Latin hypothesis.
The word quandare, by the way, also appears in works by two early Puritan writers: in Martin Marprelate, An Epistle to the Terrible Priests of the Convocation House (1588[?]):
And try if her Maiestie [Queen Elizabeth] be not shortly mooued in this suit. To it my masters roundly, you that meane to deale herein, and on my life you set the prelats in such a quandare, as they shal not know wher to stand.
and in Henry Barrowe, A Brief Discovery of the False Church (1590):
How shal these learned doctors be answered? Againe: such sacraments as are administered in the true church are alwaies true sacraments, sealing the favour and blessing of God unto them: therfore the sacramentes, but especially the baptisme there delivered (for to that above the other, these doctors have an especiall liking) is a true sacrament. What a quandare have you now brought your selves unto? You must either denie all the ministerie of the Church of England, which are not only ordeined by these bishops, but alike with them derived from the church of Rome: or els you must affirme these lord bishops to be the true ministers of the gospell; I speake in respect of their office, which then cannot be taken away: and then are all they seditious persons, disturbers of the peace of the church, and ...
Support for the Latin or quasi-Latin hypothesis
Many reference works lean toward the Latin explanation. For example, from Ernest Weekley, An Etymological Dictionary of Modern English, volume 2 (1921):
quandary. "A low word" (Johns.), first in Euphues (1579). Of obscure origin, but perh[aps] a mutation of some L. term used in scholastic disputes; cf. nonplus and F. mettre à quia, to nonp[lus, lit. to reduce to "because," both of such origin. It is explained (1582) by Mulcaster as "of a Latin form used English-like," and it seems possible that the second element is L. dare, to give.
From Eric Partridge, Origins: A Short Etymological Dictionary of Modern English, fourth edition (1966):
quandary, a dilemma, perplexity, is o[f] o[bscure] o[rigin]: ? an easing of L quam dare, how (in what manner) to give?, How much, or in what way, shall I (or you or he) give?, or a contr[action], or perh[aps] blend, of L quando dare, when to give?, When (exactly) shall I (etc.) give?, or of quantum dare, how much to give?, How much shall I give?
John Ato, Dictionary of Word Origins (1990):
quandary {16[th century]} Quandary may have originated as a quasi-latinism. One of its early forms was quandare, which suggests that it may have been a pseudo-Latin infinitive verb, coined on the fanciful notion that Latin quandō 'when' was a first person present singular form.
And from Glynnis Chantrell, The Oxford Dictionary of Word Histories (2002):
quandary {late 16th century} This word is perhaps partly from Latin quando 'when', capturing the notion of 'indecision'.
The earliest uses of the word quandary (or quandare) are now listed as being from 1577, two years before the publication of Euphues. From Georg Apperson & Martin Manser, Dictionary of Proverbs (2007):
in a quandary. 1577: Misogonus, III, i, Thou makest me in a greater quandary. 1577: J. Grange, Golden Aphroditis, sig. D3, The captaine ... standeth in a quandare, not knowing what to doe.
The uninterrupted chain of dialectal forms theory
Leo Spitzer wrote "Linguistics and Literary History" in 1945 and published it in 1948; you can find a full version of the text (including the pages not reproduced in the version that Josh61 cites in his posted question) in PDF form here. But few reference works in subsequent decades have rallied to his etymological theory.
Spitzer was not the first etymologist to see a common etymological ancestor for quandary and conundrum; Hensleigh Wedgwood, "Miscellaneous Etymologies" in Transactions of the Philological Society 1873–4 makes the same connection, although it does so in pursuit of the wandrethe hypothesis now associated with Skeat, with wandrethe leading to quandary and wandreme to conundrum.
Edward Said, "On Originality," in Uses of Literature (1973) uncritically cites Spitzer's analysis, but he seems far more interested in the similarity between the trajectory of Spitzer's essay and the story arc of Thomas Mann's Doctor Faustus than in the etymological validity of Spitzer's hypothesis about the evolution of quandary. Other academic-oriented writers invoke Spitzer's view of quandary in articles and books written in the very late 1970s (?), 1988, 2000, and 2000 (again)—but in none of those instances do they seem especially interested in whether Spitzer's etymological analysis is legitimate.
At the very least, I would be interested in reading a serious etymologist’s appraisal the "uninterrupted chain" that Spitzer traces from the French word calembredaine to quandary—namely, calembredaine conimbrum conundrum quonundrum quandorum quandary. John Ayto, Word Origins, second edition (2005) confirms that, as he puts it in his entry for conundrum:
Conundrum originally appeared in all manner of weird and wonderful guises – conimbrum, conucrum, quonundrum, connunder, etc. – before settling down to conundrum in the late 18th century. It bears all the marks of one of the rather heavy-handed quasi-Latin jokes beloved of scholars in the 16th and 17th centuries, and a mid-17th-century commentator attributed it to Oxford university. At first it meant 'whim' and then 'pun'; the current sense 'puzzling problem' did not develop until the end of the 18th century.
That certainly takes care of the second, third, and fourth links in Spitzer's chain (setting aside any question of chronological order)—but Ayto doesn't link conundrum to calembredaine nor does he mention quandary at all in the entry for conundrum.
As for quandorum, that word appears in Wright's 1857 Dictionary of Obsolete and Provincial English which offers the following brief entry:
QUANDORUM, s. A polite speech. South.
So the chain that Spitzer identifies runs through several words meaning first "whim" and then "pun" and only in the late 1700s "puzzling problem" and then to a word meaning "a polite speech" and finally to a word that, since the late 1500s meant "a question of what to do."
On that record, the evidence for Spitzer's unbroken chain seems not at all strong.
Conclusions
Most recent reference works tend to favor a Latin or quasi-Latin origin for quandary, and that hypothesis seems far more plausible to me than Leo Spitzer's suggestion involving a series of dialect forms originating with the French word calembredaine and continuing through conundrum to quandary—a notion that raises serious questions involving chronology and contemporaneous meanings. The wandreth theory, favored by Walter Skeat in 1888, lost its chief proponent by 1905, and the straight-from-French "Qu'en dirai-je?" etymology fell out of favor even earlier.
