(SEE ADDITION BELOW MY ORIGINAL ANSWER)
It seems that the transferred sense of "métier" in English has first been "loosened" (as is apparently usually the case) in the sense of "expanded" to include the notion "in which one is specially skilled," (which notion is, in my opinion, missing in all the original French meanings), and then curiously "(re)-tightened" to mean that, and only (or primarily) that newly expanded sense.
Therefore, based primarily on your analysis of the word's meanings, I'd say that "métier" in French does not fully (or at least not automatically) capture the notion of "specially skilled" (although "rôle," as you state, comes close, as does, in my opinion, "Homme du métier, homme qui se connaît à une chose ; être du métier, se connaître à une chose.")
To find an option in French that kind of captures this "specially skilled" notion, I started with the rather curious use of "line" in the cited NED extract and arrived at "un/mon/son rayon", which according to my Le Robert-Micro can mean: 3/III/2. "Domaine particulier. 'Je regrette, ce n'est pas mon rayon, ce n'est pas de ma compétence...'"
To make a connection from "rayon"/"line" back to the two cited English uses, I suppose that one could simply use "line" or "line of work," but they wouldn't necessarily capture the "specially skilled" notion, so maybe "line of expertise" would work, although that might be going a bit beyond the notion of "specially skilled." ("line of expertise" makes me think of "field of expertise" or even just "field" to replace "métier" in English, but I'm not sure how to connect "field" to "rayon" to get it back to "métier" in French)
ADDITION:
Upon further reflection, I think it’s worth noting that both of the examples you give of the use of “métier” in English involve religious vocations/functions. Furthermore, as you and the cited ELU answer both note, the usage of “métier” in English dates from 1792, from which one could deduce that Charlotte Smith was the first to so use it. Being the first and therefore defining user of it, perhaps an examination of the possible reasons behind her decision to use it as she did, in a “religious vocation/function” context, might shed some light on both the English and French issues.
Normally I would first think of using “calling” when discussing religious vocations and functions in English and I think that it’s possible that the two authors, especially Smith, being the word’s first borrower, were simply looking for a suitable word to replace “calling” in their respective religious (borderline sacrilegious?) contexts.
For whatever reason, instead of coming right out and using the English “calling,” with its “heavenly” connotations, along side of the arguably incongruous notion of “mortal aversion to,” in the 1792 example and along side of the arguably overly enthusiastic description of “heretic-burning” in the 1842 example, the authors turned instead to the French “métier,” thinking, based perhaps on their awareness of the word’s “service religieux”/ («le service divin (spirituel, liturgique, pastoral)» origins, that “métier” adequately captured the religious vocation/function (l'appel à [or de] Dieu) sense of “calling” that they were after, no more no less.
In my mind, it's arguable that the use of “métier” in purely religious contexts to capture the full “religious vocation/function” sense of “a calling for which one is especially fitted” technically doesn’t require expansion of its meaning in French; it simply requires knowledge of and reversion to the word’s original “service religieux” meaning, with the “special fitness” being implied. Implied, because who, at least at the time of the word’s origins (881?), would have dared to question one’s fitness when “the call” came from the Big Guy/Gal Him/Herself?
Expansion upon the French meaning, however, is required when “métier” is used in English outside of purely religious contexts, and it’s possible that this expansion to include the notion of “[non-devine/quasi-devine] callings/vocations/functions for which one is especially fitted” could be best captured in French by words that have both purely “ecclésiastique” meanings as well as non-(or at most quasi-) “ecclésiastique” meanings.
With this in mind, I now propose two new candidates as possible answers to your question.
The first new candidate that would seem to contain the above dualism is “état,” (4-Profession, condition) which my “Le Robert & Collins” French/English Dictionary (1999) lists as the second of two translations of “calling” (after vocation), and which under meaning II:- B.- 2. here at cnrtl.fr has both purely religious and non-religious senses:
II.− Situation d'une personne du point de vue de l'ordre social.
B.-[Sur le plan soc.]
2 . P. méton. Profession, travail, tâche. Apprendre, avoir, embrasser, prendre un état; faire son état; horloger de son état :
- L'état de charpentier m'a toujours plu. « L'état de charpentier! s'écria mon oncle avec une sorte d'explosion de joie, tu n'es vraiment
pas dégoûté. Je ne t'en aurais jamais indiqué un autre. Le
charpentier, mon enfant, c'est dans ses chantiers que notre divin
Maître a daigné choisir son père adoptif... » Nodier, Fée
Miettes,1831, p. 72.
♦ État ecclésiastique, militaire. Parmi les
métaphysiciens françois qui ont professé la doctrine de Locke, il faut
compter au premier rang Condillac, que son état de prêtre obligeoit à
des ménagements envers la religion, et Bonnet, qui, naturellement
religieux, vivoit à Genève dans un pays où les lumières et la piété
sont inséparables (Staël, Allemagne,t. 4, 1810, p. 56).Il [l'oncle
Edme] exaltait l'état militaire, l'honneur des officiers, la vertu des
Jacobins et distribuait des pièces d'argent à ses jeunes auditeurs
s'ils promettaient de combattre, plus tard, pour le roi de Rome (Adam,
Enf. Aust.,1902, p. 191).
I ran across my second new candidate, “sacerdoce” (4-(Figuré) Vocation), in the “etymology/history” section near the bottom of the cnrtl.fr site you provided for “métier.” “Sacerdoce” was totally new to me, which explains why I needed to look it up and in the process discovered that it has the "requisite" dual, religious & non/quasi-religious, meanings.
For “sacerdoce,” cnrtl.fr gives the following, quasi-religious meaning in which the word “vocation” is given as a synonym (which gets me back to my old “Le Robert & Collins” French/English Dictionary and its first entry for “calling”):
− P. anal. Fonction qui revêt un caractère quasi-religieux par la
vertu et le dévouement qu'elle exige. Synon. vocation. Sacerdoce
politique; sacerdoce de la magistrature, du professorat; s'acquitter
d'une tâche comme d'un sacerdoce. Ces guides du Sahara sont des
personnages respectés (...) ils exercent une sorte de sacerdoce
(Sainte-Beuve,Nouv. lundis, t. 9, 1864, p. 119).Mon respect s'accrut
pour ce saint homme dont le dévouement ne trouvait pas de récompense:
je fus préparé de bonne heure à traiter le professorat comme un
sacerdoce et la littérature comme une passion (Sartre,Mots, 1964, p.
33).
− P. métaph. Je crois que mes vieux frères [les républicains]
doivent frapper de grands coups, et que vous [les saint-simoniens],
revêtus d'un sacerdoce d'innocence et de paix, vous ne pouvez tremper
dans le sang des combats vos robes lévitiques (Sand,Corresp., t. 1,
1836, p. 342).
To the extent that even the non-religious/quasi-religious sense of “sacerdoce,” all by itself, might seem too strong to identify and capture the missing French meaning of “métier” that you seek, perhaps you could still look to the above entry from cnrtl.fr and, although not single words, use one of the following curious phrases contained therein: “comme [d']un sacerdoce” or “une sorte de sacerdoce.”
Using my two new candidates in your examples would give the following (although, as I tried to explain above, I think the original “service religieux” French meaning of “métier” for contexts involving "religious vocations/functions," such as these, doesn't necessary need to be expanded):
with "état":
1792 CHARLOTTE SMITH Desmond I xiii 253 They wanted, indeed, to make
me a monk; but I had a mortal aversion to 'that métier/calling' (=
'cet état').
1842 BARHAM[...] Heretic-burning - in fact, 'tis 'his métier/calling'
(= 'son état').
with "sacerdoce":
1792 CHARLOTTE SMITH Desmond I xiii 253 They wanted, indeed, to make
me a monk; but I had a mortal aversion to 'that métier/calling' (=
'cet (le) sacerdoce').
1842 BARHAM[...] Heretic-burning - in fact, 'tis 'his métier/calling'
(= 'son sacerdoce').
and finally with “comme [d']un sacerdoce” or “une sorte de sacerdoce.”
1792 CHARLOTTE SMITH Desmond I xiii 253 They wanted, indeed, to make
me a monk; but I had a mortal aversion to 'that métier/calling' (=
'cette sorte de sacerdoce').
(this one shows well, I think, that "métier" (in its original sense of
"religious service") really doesn't need to be replaced/expanded upon
in this context, at least not by the quasi/non-religious sense of
sacerdoce, but then again its ambiguous use here could help the author
to emphasize the disdain/sarcasm that her character exhibits towards
monks (or at least towards being one) that the use of "mortal aversion
to" clearly implies to me)
1842 BARHAM[...] Heretic-burning - in fact, 'tis 'his métier/calling'
(= [c'est] 'comme son sacerdoce').
