I only quoted translations because you mentioned “a pretty standard translation”, and the “standard translation” seems in fact the opposite. But I much prefer going to the Greek cites. Here are a few.
θάμβησέν τ’ ἄρ’ ἔπειτα ἔπος τ’ ἔφατ’ ἔκ τ’ ὀνόμαζε·
δαιμονίη, τί με ταῦτα λιλαίεαι ἠπεροπεύειν;
This is somewhat adversarial speech, but also polite and to a goddess. I suggest that the term distances the statement and keeps the reproach from becoming bitter. And notice that θάμβησέν. The scholia often suggest θαυμάσιε and μακάριε for general synonyms to δαιμόνιε, neither of which are taken especially literally in address.
A bit after the book 6 passage we’ve been looking at, Hector to Paris.
τὸν πρότερος προσέειπεν Ἀλέξανδρος θεοειδής·
ἠθεῖ’ ἦ μάλα δή σε καὶ ἐσσύμενον κατερύκω
δηθύνων, οὐδ’ ἦλθον ἐναίσιμον ὡς ἐκέλευες;
Τὸν δ’ ἀπαμειβόμενος προσέφη κορυθαίολος Ἕκτωρ·
δαιμόνι’ οὐκ ἄν τίς τοι ἀνὴρ ὃς ἐναίσιμος εἴη
ἔργον ἀτιμήσειε μάχης, ἐπεὶ ἄλκιμός ἐσσι·
ἀλλὰ ἑκὼν μεθιεῖς τε καὶ οὐκ ἐθέλεις· τὸ δ’ ἐμὸν κῆρ
ἄχνυται ἐν θυμῷ, ὅθ’ ὑπὲρ σέθεν αἴσχε’ ἀκούω
πρὸς Τρώων, οἳ ἔχουσι πολὺν πόνον εἵνεκα σεῖο.
This is gentle and merely contradicts Paris’s self-reproach. The δαιμόνιε is not calling him strange or crazy, but instead lightens the statement.
Here, everyone has decided that it’s time to think about home, and nothing separates Odysseus in the situation:
ὣς ἔφαθ’, ἡμῖν δ’ αὖτ’ ἐπεπείθετο θυμὸς ἀγήνωρ.
ἔνθα μὲν ἤματα πάντα τελεσφόρον εἰς ἐνιαυτὸν
ἥμεθα δαινύμενοι κρέα τ’ ἄσπετα καὶ μέθυ ἡδύ·
ἀλλ’ ὅτε δή ῥ’ ἐνιαυτὸς ἔην, περὶ δ’ ἔτραπον ὧραι
μηνῶν φθινόντων, περὶ δ’ ἤματα μακρὰ τελέσθη,
καὶ τότε μ’ ἐκκαλέσαντες ἔφαν ἐρίηρες ἑταῖροι·
δαιμόνι’, ἤδη νῦν μιμνήσκεο πατρίδος αἴης,
To call this a reaction to an unreasonable or exaggerated action, seems, well, like an unreasonable or exaggerated statement.
I have a few more (ψ166, 174, 264, ξ443) but look at the end of the Iliad:
ἐς δ’ ἄλοχον Ἑκάβην ἐκαλέσσατο φώνησέν τε·
δαιμονίη Διόθεν μοι Ὀλύμπιος ἄγγελος ἦλθε
λύσασθαι φίλον υἱὸν ἰόντ’ ἐπὶ νῆας Ἀχαιῶν,
δῶρα δ’ Ἀχιλλῆϊ φερέμεν τά κε θυμὸν ἰήνῃ.
There is no sort of reaction of any sort here. This is pure tenderness and politeness.
The easiest case to make, I think, and I’m backed up by many readers, is that this is a polite word reserved for delicate situations. Emotional speech with a marriage partner. Speaking to a stranger, where it means something like “good sir”. It is distancing language, and as the scholia say, works very similarly to how θαυμάσιε is so often deployed by Plato.