After having now gone through the material, here are my thoughts. To preface this, I'm only proposing the various means by which this semantic shift could have taken place, not deciding between them. Thus, I'm only answering the procédé part of your question.
The two basic paths I'm laying out are either (1) that de valeur either had or came to have the sense of fort, extraordinaire, which then swung over to the negative side instead of the positive thanks to the inherent neutrality of that sense, or else (2) that it did have a positive meaning, but irony flipped its valence, as you suggested. Clearly there is some overlap between these two stories.
Bossu's gloss and the Muskogean original
First, I think Papa Poule is on the money with his second interpretation of de valeur as it occurs in Bossu's text. Bossu's gloss for the word makes little sense in context (though it might have if the opening of the "harangue" weren't immediately followed by "mais").
Since the idea of valeur is tied to the verb valoir and can mean ce que vaut une chose (TLFi étymologie), it makes good sense to me that the father is saying, "It is indeed fitting/warranted that my son should die, but being young and vigorous, he is more capable [than I] of providing for his mother, his wife, and his four young children."
However, the scenario is complicated by the ambiguity of Bossu's footnote:
Le terme de valeur est un mot qui signifie, en leur langue, ce qui est fort ou extraordinare.
The linguistic layers must be disentangled. Presumably by "in their language" he means one of two things: a patois or dialect of French, which I doubt; or the Acolapissas' own Muskogean language, in which case our only access to the Muskogean term is by the intermediary of Bossu's rendering de valeur. However, the point of Bossu's footnote is to say that the literal meaning of de valeur does not represent the meaning of the Muskogean, giving us little clarity indeed about the latter.
It seems that Bossu considers that the Muskogean in some sense (etymologically?) equates to de valeur at the time of his writing, yet actually conveys the meaning "ce qui est fort ou extraordinaire". That is, his observation is about of the same order as the French learner who reports that aujourd'hui "literally" means "on the day of this", but what it really means is "today".
This sort of astonishment is very typical of an early learner navigating a second language and realizing that many simple words can be broken down by an analytical eye into a curious "literal" meaning. (Indeed, it's an essential strategy for identifying the meanings of new words.) That Bossu was often struck by words of this kind is suggested by the avertissement :
...d'autres [notes] pour expliquer certaines phrases emblématiques dont se servent les Sauvages dans leurs harangues.
By this I mean that just as a native French speaker uses aujourd'hui simply to mean "today" without thinking of the components that stand out to a language learner, for all we know the Muskogean word may have resembled de valeur in form only. If that's true, de valeur was no more the best translation than "on the day of this" would be for aujourd'hui — though it may be of etymological interest.
Proposed intermediate stage: "fort, extraordinaire"
What is the significance of the Muskogean for our etymology? It contributes the first of the several hypothetical ways that de valeur could have come to mean fort, extraordinare.
Perhaps settlers were just as struck as Bossu was by the "literal" meanings of those phrases emblématiques, and allowed these meanings to creep into their language. This phenomenon is referred to as semantic borrowing. Bossu demonstrated it very well: he used the French phrase in what he felt was an unnatural way that must be explained to French readers, with the intent of mimicking the phrase's semantic range in Muskogean. Incidentally, this effect has a long history: as Moises Silva notes in a 1975 article on semantic borrowing in the New Testament, the Septuagint Greek that translated the Hebrew Tanakh used Greek terms as though they were the Hebrew equivalents: for example, they used one Greek word for "lake" and "sea" as Hebrew does, rather than distinguishing the two as Greek did. No new word need be borrowed for the semantic range to spread. Hence, it would not be surprising if by long cultural association, Canadian French speakers tended to borrow not only the forms but sometimes the semantic ranges of Indigenous words.
Perhaps, on the other hand, Bossu's account and others like it could have influenced de valeur. That is, the semantic range might have shifted in Canadian French without direct reference to the Muskogean, only mediated.
Perhaps in Canadian French (or that of the original settlers' home regions when they left France), de valeur still had a neutral sense similar to one of the meanings of its root, Latin valeō : with "être significatif, puissant". Compare even the modern senses noted in TLFi entry IV - D "Importance, portée d'une chose" or I - B mettre en valeur, one of whose senses is "mettre en évidence, en relief". On this view, the Muskogean term is entirely irrelevant, since de valeur would not have gained but retained this meaning.
Between the above, I consider (1) more likely than (2), but between (1) and (3) I would be undecided.
However, I reflect at this point that after consideration of the TLFi entry and of valeō, as well as similar terms in other languages, either way there is some semantic overlap between "to be worth, to signify" and "to be strong, to be noteworthy". Expressing something's worth is not far removed from saying that it's worthy, nor identifying its signification from saying that it's significant. (Incidentally, this is another demonstration of the principle that the pragmatic value of an utterance gradually colours the denotations of the words used.)
In light of that, we can add the remark that Bossu hardly needed to provide his interpretation for de valeur at all — unless the meaning was firmly positive by that point and hence ill-fitting in the father's remark. For example, it might have come primarily to mean "valuable" or even "excellent".
On the one hand, this is plausible given that the TLFi etymology of valeur lists mostly positive senses long before the 18th century. On the other hand, it would mean that the "literal" meaning of Muskogean term had such a positive connotation, which is harder to reconcile with its appearance at that juncture, though not impossible, if Bossu's analysis is correct (but remember that his particular interpretation hurts the text's coherence!).
In any case, I think we're obliged to posit this fourth option:
- There never was a fort, extraordinaire stage natural to Canadian French. It was only positive.
Ending up at "unfortunate"
As I mentioned in my comments, the semantic area of "significant, notable" is highly ambivalent in terms of sentiment. And as you mentioned, irony or antiphrase can swing the valence of a term. Those seem to me to be the two plausible paths to a negative meaning.
- If there was a "fort, extraordinaire" stage (1–3 above), it was probably ambivalent as to whether it was positive or negative. Such terms tend to fall on one side or the other over a language's lifetime, and even to swing between them at different stages. In fact, such developments have been very common in English:
enormous : previously "abnormal", even "outrageous" (compare enormity); now "huge" (neutral)
outstanding : previously "conspicuous" (compare standing out); now "excellent, admirable"
anomalous : neutral, yet sharing an etymology ("against norms") with the negative term abnormal
extraordinary : literally "out of order"; now "excellent" (or neutral "noteworthy")
egregious : literally "out of the flock"; in Latin it meant "exceptional"; the early English borrowing meant "outstanding, distinguished" (positive); modern English "heinous" (negative)
- If, on the other hand, there never was a "fort, extraordinaire" stage (4 above), irony or antiphrasty could indeed have swung a positive connotation to a negative one.
What is needed to determine whether, which, when, and why either of the above developments happened is a good corpus crawl. For example, either examining Ngrams results by hand or subjecting them to natural language processing sentiment analysis.
This of course is the historical, contingent question; I hope that I've answered the theoretical, procédé question. I'm not sure if there's a term reserved for this process, but "polyvalent" is the first word that comes to mind for these words that are liable to undergo it.
Appendix: phonological slip
Since the 1930 document and WordReference thread both mention the connection with malheur and male heure, it's worth examining this account of the change, though I think it's less likely.
The sounds [v] and [m] are not the most easily confounded. However, [v] is just the endpoint of a French sound that may have been at an earlier stage in its development when de valeur took on this meaning. Two candidates come to mind for sounds that could be confounded with [m].
The first is the origin of this phoneme, Latin /u/ (realized as [w] before a vowel). The reason /u/ [w] is a good candidate is that it involves bilabial movement. From what I can recall about the phonological development of French, however, it's very unlikely that the phoneme would still be realized [w] in the 18th century — or even in a regiolect of earlier settlers in the 15th–17th centuries. I was looking for references and the only readily scanned one was this Wikipedia article, which is somewhat vague on /u/ but does imply that it had shifted to /v/ long before the New World was discovered.
The second is the voiced bilabial fricative [β]. This is a very predictable step between [w] and [v], bridging the two by combining the bilabial articulation of [w] (the condition for confounding it with [m]) with the frication of [v]. In fact, [β] is the endpoint of /v/ in some phonological conditions in many variations of Spanish. It's even possible that it was present in some older or regional varieties of French, because to speakers whose languages don't possess the sound, it tends to be perceived as [v]. Data from that period might not make the distinction clearly, so it's theoretically possible that valeur sounded more like malheur in the settlers' dialects than it does now.
Moreover, it's true that slips of articulation or perception can spread across a language. For example, the English phrase home in on soon spawned hone in on because it's an extremely good candidate for assimilation, and it now appears that original phrase could be being overtaken.
However, I have two reservations about this explanation in the case of valeur / malheur. In the first place, we'd expect to see many more words showing /v/ alternating with /m/, and probably some research on such a phenomenon.
In the second place, whereas "home in on" and "hone in on" have the same meaning (if the latter means anything), it seems unlikely that a tendency to mistake valeur for malheur would go remarked long enough to become entrenched given how directly opposite they are — the observation that launched this question.
Between those points and the semantic overlap theory, I wouldn't stake my bet on this explanation.