In a bit of e-mail dialogue yesterday and today, I ended up writing a rather lengthy explanation of my thoughts on the consonant clusters χθ and φθ word medially and their pronunciation/phonology. I hold, following Mussies that these two clusters were pronounced /kth/ and /pth/ in the Hellenistic Period.
Note: Everything in // is phonemic IPA and everything in  is phonetic IPA. Anything outside brackets that looks like Greek is Greek.
Without spending too much time looking (I’ve seen it in a few places), Gerhard Mussies writes on word medial consonant clusters (with somewhat idiosyncratic terminology),
“Explosive plux explosive. both are either voiced or unvoiced. The first cannot be aspirated: -φθ- and -χθ- are misleading orthographies and respresent resp. -pth- and -kth-. the second consonant is always a dental explosive, the first either a labial or a velar explosive: -bd-, -pt-, -pth-, -gd-, -kt-, -kth-”
(Morphology of Koine Greek [Leiden: Brill, 1971], 51).
Not much for argumentation. But as I understand it, it’s the same case for Modern Greek. So on the assumption that φ in the Classical period was /pʰ/ rather than /f/, then it’s a pretty reasonable development. Classical Greek has a phonemic alternation between the non-aspirated stops /p, t, k/ with aspirated versions /pʰ, tʰ, kʰ/ (cf. also HERE). Non-Alveolar Stop + Aspiration + Alveolar Aspirated Stop is both difficult to pronounce and also phonologically implausible, which is what I had intended. My mistake was that in my writing I had forgotten that θ wasn’t a fricative either during that period. I would anticipate a rule for the Classical period to be something like:
pʰ (Gk: φ) –> p / _tʰ (Gk: θ)
In English this means: the phoneme /pʰ/ is realized as the phone [p] when it precedes /θ/. This is confirmed by Allen when he writes (in arguing that the Classical φ, θ, χ were aspirated stops, not fricatives):
Further evidence comes from the procedure of ‘expressive doubling’ of consonants (as in e.g. ‘familiar’ ἄττα, ‘hypocoristic’ Δικκώ, ‘imitative’ ποππύζω). For when the doubled consonant is φ, θ, or χ, the resulting form shows πφ, τθ, κχ–e.g. ἀπφῦς, τίτθη, κακχάζω. Such a spelling indicates that the lengthening of these consonants consisted in a stop* element (π, τ, κ), which would not be appropriate if the original sound were a fricative, but entirely so if it were a plosive: thus [ph, th, kh –>[pph, ttph, kkh].
Buth (HERE, 5) holds that it’s unclear whether the voiceless /pʰ, tʰ, kʰ/ had changed to the ficatives /ɸ, θ, x/ by the time of the NT — definitely by the end of the Roman period. This actually suggests that a transliteration from BDF (“צָֽרְפַת becomes Σάρεπτα Lk 4:26 (-φθ- B²KLM) as in the LXX (-φθ- is a weak variant)” [BDF §39(2)]) was probably the difference between aspirated and non-aspirated stops, rather than stop/fricative.
In terms of the order of that the voiceless stops themselves changed to fricatives, we have other evidence. If /pʰ/ was first go to /f/, then the cluster /-ftʰ-/ would violate sonority sequencing (Burquest, Phonological Analysis, 147ff.), that is, the prinicple that the syllable is layered in a way with the least sonorant phones appear farther to the outside: [p] –> [pʰ] –> [ɸ] –> [h] –> vowel. And while it is possible for an individual consonant to simply ignore sonority sequencing (e.g. /s/ in English: stop rather than tsop), this is actually rather rare across languages. In fact, it is peferrable phonologically to treat the English /s/ in these cases as extra-syllabic, “because they function like a minor wave of syllabicity outside the main wave (Burquest, 152).
If /tʰ/ changed to /θ/ first, then the question is whether it was pronounced /pʰθ/ or /pθ/. The former is rather unlikely since aspiration ([h]) is higher on the sonority scale than fricatives. Instead this fact actually makes /pθ/ more plausible since, phonologically speaking, the rule:
/pʰ/ –> [p] _/θ/
can explain things both in the diachronic development for the cluster φθ and also the synchronic system before the aspirated stops became fricatives a various points along the way.
Also, searching BDF for instances of φθ, it looks like in the transliteration of foreign words there’s a bit of evidence (with the caveat that such things are shaky evidence): “צָֽרְפַת becomes Σάρεπτα Lk 4:26 (-φθ- B2KLM) as in the LXX (-φθ- is a weak variant)” (BDF §39).
In general, all of this thinking about phonology makes me want to sit down and read William Sidney Allen’s Vox Graeca — especially after perusing it’s limited (used restrictively) pages on Google books this afternoon.
Allen, William Sydney. Vox Graeca: The Pronunciation of Classical Greek.
Burquest, Donald A. Phonological Analysis: A Functional Approach. 3rd Edition. Dallas, Tex.: SIL, 2006.
Mussies, Gerhard. The Morphology of Koine Greek as Used in the Apocalypse of John: A Study in Bilingualism. Novum Testamentum Supplement 27. Leiden: Brill Academic Publishers, 1971.