My thoughts on the various contenders:

Forget testimony of post-classics. If ζ became [z] long before they were born, how could they possibly know? What factual proof is their testimony based on? Why should we find reference to the pronunciation of the letter ζ in pre-Hellenistic Greek writings? The Greeks weren't yet trying to teach the barbarians a more civilised tongue. No "Teach Yourself Attic Greek Pronunciation in a Week" books yet. Written by mother-tongue pre-Hellenistic Greeks of course.

Forget Erasmus He just came up with a novel theory, in contradiction with what went before. But doesn't seem to have come up with any proof substantiating his hypothesis.

Aristotle and his elements/letters s, d and a. This seems good enough proof for the fact that ζ was not yet pronounced [z] but a combination of σ and δ. I think he was talking about composition, not sequence. 3 separate elements either keeping their individuality or combining to produce something new.
I did agree that this might be considered a plausible proof in favour of /sd/ till, reading on about Bonitz and Bekker's interpretations got me wondering about what Aristotle himself had actually written/meant.
It is very important to keep in mind that what applies to the NT, applies here too. Copiers are human. Humans make mistakes. Therefore copiers make mistakes. I would hesitate to take as proof a single occurrence of something that looks like proof, but is at the mercy of a copier's concentration, attention and understanding. Can we be sure that Aristotle actually used the letters in the order given? that the man copying understood
i) what Aristotle meant and
ii) that therefore the order might be of importance?
I wouldn't bet on it.

1.5.3

1. The nasal sound [n] is "sometimes" dropped before alveolar fricative [s] if that [s] is followed by a plosive (κ-χ, π-φ, θ-τ). (for examples see συ-σ... in a lexicon). Not δ because, according to Allen himself, sigma can only be [z], not [s]. Now where did he get that information from, as there are not many words spelt σδ besides τούσδε, τάσδε. Which could both very easily be pronounced tou[s]-de, ta[s]-de as they belong to 2 syllables/words.
   For "sometimes": see dictionary for examples with the prefix ἐν- followed by sigma anything, [n] doesn't budge.
   See also ἄνσχετος (not ἀνά-σχετος despite the fact that it is the verbal adjective of ἀν-έχω short for ἀνα-έχω, I bear, suffer endure.)
   
2. Before [s] followed by a vowel συν- changes to συσ- but ἐν- stays ἐν-:
   συν +σιτέω becomes συσ-σιτέω (to mess with),
   συν + σῴζω becomes συσ-σῴζω (to help in the saving) etc

1.5.3.3. Allen: Internal Evidence: Ancient Greek Writing of Non-Greek Words

This is no proof, because we all get foreign names wrong, even easy ones. In Spanish Algeria is Argelia. Spanish 'pre'guntar becomes 'per'guntar in Portuguese. Why then couldn't "Auramazda" have become "Auramadza", the difference in sound is not that enormous. And if you're used to hearing [dz] at the beginning or end of syllables, then you'd have a definite tendency to change [zd] to [dz].
This occasional inversion of sounds could also account for the the PIE root *osdo- becoming Greek "ὄζος" even if ζ was pronounced [dz]. Again, not acceptable as proof.
And look what I found in Liddell: ὄσδος, ὄσδω - Doric and Aeolic for ὄζος, ὄζω. Spelling variations in ancient Greek always reflect pronunciation, cf. epic and ionic η instead of α in female noun endings, doric ν instead of Attic λ (e.g.ἦνθον instead of ἦλθον, I came), doric πρὸς τῶν σιῶν instead of θεῶν et al.

1.5.4.3. Allen: Linguistic History: Proto-Greek */ds/

"While { Woodard, 161-162} cites three cases in which a derivative /ds/ might be expected, { Allen, 56} gives only two: PIE *-dy- and *-gy-.
Thus, for example, Greek "πεζός" apparently derives from PIE *ped-yos, which would suggest [pe̞dzos] (Allen voices ds to [dz]) rather than [pezdos].
{ Sturtevant, 92} cites these two PIE roots as well."

This, to me, looks like a beautiful proof for the need to have a special letter [dz], since the pronunciation of pe[dz]os could not be rendered by the combination of δ+σ, as sigma is always voiceless before a vowel.

1.7.4.3. Woodard: Historical Linguistics: Nasal Loss

1. We're back to the 1.5.3 as far as [dz] is concerned.
   
2. Is "nasal + t + s" an exception to his rule? [n] and [t] are dropped and the vowel is lengthened or changed into a diphthong:
   e.g. ὁ γίγᾱς, τοῦ γίγαντος, τοῖς γίγᾱσι (for γίγα-ντσ-ι)
   e.g. ὁ γέρων, τοῦ γέροντος, τοῖς γέρουσι (for γέρο-ντσ-ι)
   There are masses of examples of a dropped ντ combination in front of voiceless [s], but none for νζ either [ndz] or [nzd]
   I don't find his argument conclusive at all. But see what happens in modern Greek:
   

   Slave languages have lots of words with the [zd] combination, none of them derived from Greek and all spelt with the 2 separate letters [z] (not s) and [d]. Only languages with a special letter for voiced [z] can start words/syllables with the oral combination [zd].
   Not Greek though, because in modern Greek δ is pronounced [ð] like (the, this etc.), whereas the sound [d] is spelt ντ (sometimes read [nd]). [zd] would have to be written ζντ.There are no words using this combination.
   But the Greeks still have the [dz] sound: as ζ is now pronounced [z] they'd have to write a νt in front of it to produce the [dz] sound. And see what happens: the ν of ντζ is dropped, exactly as could have happened with Allen's σύζυξ, even if σύζυξ stood for σύ[dz]υκ.
   This [dz] is however only used in words acquired from foreign languages, mainly Turkish of course, and is an approximation of the [ʤ] sound the Greeks find very difficult to produce. (cf. proto-Greek in 1.5.4.3)

1.10. τούσδε

I've got some more for you:
ἀπροσ-δόκητος, unlooked for
δυσ-δαιμονέω, I am unfortunate
σ ending one syllable, δ at the start of the next. Exactly what happens when we find the sequence κ-σ (e.g. ἔκ-στασις, a standing outside; transe) not ξ, because it isn't eks-tasis but ek-stasis.
That is also why 'I seek out' ἐκ-ζητέω is no proof for either [dz] nor [zd] defenders.
These words don't invalidate the theory that ζ was pronounced [zd], are not proof that ζ had to be [dz], but they seem to prove that if 'to Thebes', according to Liddell is Θήβασδε (spelt σδ) !!?!! (in the Illiad 23.679)
then to Athens would also have been spelt Ἀθήνασδε. If it were pronounced that way.
And 'to(wards) the ground' is χαμᾶζε. If that were pronounced χαμάσ-δε, it would mean there was such a word as αἱ χαμαί. I haven't found one. And the locative, 'on the ground' would be, according to the Ἀθήνησι (in Athens) pattern: χαμῆσι or maybe χαμᾶσι. But it isn't, it is χαμαί. Who says languages are boring?

Now to ἀσπίς, ἀσπίδος dative plural ἀσπίσι

Why not ἀσπίζι following the examples of φύλαξι and κλωψί? Because dative plural always ends in voiceless [si] (even 1st and 2nd declension words originally ended in -aisi/oisi).
Instead of φύλαξ take αἶξ, αἰγός (a goat) and instead of κλώψ take φλέψ, φλεβός (a vein). Dative plural αἰγσί, being pronounced aiksi is written αἰξί, and flebsi, pronounced flepsi is written φλεψί.
Now, just as [b] changes to [p] and [g] to [k], so [d] changes to [t] if followed by voiceless [s]. ἀσπίδσι would be pronounced [aspi-tsi] and could therefore not be written ἀσπίζι. Anyway, as any dental plosive is dropped in front of [si], δ, θ as well as τ, we have, quite normally: ἀσπίσι. The same goes for ὁ παῖς, τοῦ παιδός, τοῖς παισί (for παιδ-σί) to the children, δ pronounced [t] dropped because followed by voiceless [si].

Now to some more thoughts, of my own. In defense of [dz] this time. After all this reading and pondering I've come to the conclusion that ζ was more than probably pronounced [dz] till the [d] was eventually dropped.
Why? Because you showed me the basic flaw: there wouldn't be any need for a special letter [zd], since Allen states quite clearly that σδ was pronounced [zd]. But you can only have a [dz] sound by introducing a special letter.
Why?
Because sigma followed by a vowel is always voiceless [s], in Greek that is, ancient as well as modern.
Since βσ, πσ and φσ are all pronounced [ps] why not use one letter for those 3 combinations? - ψ
γσ, κσ and χσ, all pronounced [ks], one letter: - ξ.
By analogy δσ, θσ and τσ would then all be pronounced [ts]. But in ancient Greek dental plosives were dropped before voiceless [s].
Therefore the only way to a write a [dz] sound would be to have a special letter for that sound.
Since there is no need for a special letter to write the [zd] combination - σ is pronounced [z] before β, γ and δ - I would think that the special letter ζ was created to represent the impossible to write δσ [dz] sound.

Some languages have a special letter pronounced [ʤ], because they haven't got a letter pronounced [Ʒ]: English j, Turkish c
a special letter pronounced [ʧ] like in child because they have no letter h but a [ʃ] (sh) sound: Russian (Slave languages) ɥ, Czech č, Turkish ç.
Italian is the only western language with a letter z pronounced [dz]. And Chinese, when written with our alphabet (pinyin) uses the letter z to represent the sound, guess what... [dz].
Russian does have a special letter that is pronounced [ts] (ц). As do the Germans (z), the Czech (c), the Hungarians (c), the Hebrews (צ).
And Japanese words are not spelt using letters but kanas (syllables) (49 of them, though for some reason the table is called 50-sound table). When importing foreign words they make them fit their way of pronouncing: station = su-tê-shi-o-n, sports-car = su-pô-tsu-kâ etc. The only double letter that can be expressed by one kana is "tsu", all other 2 consonant combinations are spelt using 2 kanas.

None of the languages I've come across has a special /st/ letter, i.e. every /st/ combination in every language I've come across is spelt using 2 letters: st or zd (if there is a special [z] letter, like in Slave languages for instance).

Conclusion:

I therefore find it highly unlikely that the ancient Greeks pronounced ζ [zd]. And, because of Aristotle's ζα making it clear that ζ was a double sounding letter, I am now pretty confident that pre-Hellenistic Greek ζ was actually pronounced [dz]. Which I wasn't before reading these "proofs" to the contrary. Thank you for providing me with all this information that allowed me to clarify my ideas.