What evidence is there for the classical pronunciation of zeta?

W. Sidney Allen's famous Vox Graeca, which is well worth the time of anyone with a more-than-casual interest in Greek pronunciation, has three-and-a-half pages' worth of things to say about the subject, which I will attempt to summarise.

It's uncontroversial that from quite early in the Archaic period through the late 4th century BCE, ζ represented [zd] in every major dialect. Evidence for this:

1. The combinations Ἀθήνας + δε, θύρας + δε are written Ἀθήναζε, θύραζε.
2. In most dialects, including Attic, a nasal is regularly lost before fricative σ, so e.g. where the ν of συν is preserved in σύνδεσμος, it is lost in σύστασις. The same loss is found before ζ, e.g. σύζυξ, σύζῆν, and in πλάζω next to ἔπλαγξα, suggesting the sound following the nasal was a fricative.
3. In some cases ζ derives from PIE *sd [zd], as in ὄζος < PIE *h₃ósdos (cf. German Ast), ἵζω < PIE *si-sd-oh₂ (cf. Latin sīdō, which instead lost the second s of the same form, with compensatory lengthening of the i). (n.b. Allen has forms without laryngeals here.)
4. Up until the early 4th century, ζ is used to render Iranian zd, e.g. Ὠρομαζης = Auramazda (Plato), Ἀρταοζος = Artavazda (Xenophon).

However, before it was [zd], it was likely [dz], because:

1. More often than deriving from PIE *sd, ζ continues PIE *dy or *gy, e.g. πεζός < PIE *ped-yos, ἅζομαι beside ἅγιος. These groups must have developed through an affricate stage [dʒ] > [dz] (cf. Latin medius > Italian mezzo) before becoming [zd] through metathesis.
2. It's difficult to see why ζ would exist at all when σδ would do fine for [zd]. δσ is not a satisfactory representation of [dz], however, since voice assimilation is typically regressive rather than progressive in Greek.
3. Forms of zeta are used with probable value [ts] in the Oscan and Umbrian alphabets, based on the Euboean Greek alphabet of ~700 BCE. It may have the same value in some early Cretan inscriptions.

The metathesis of [dz] into [zd] isn't rare and would be particularly natural in Greek, which didn't have any other affricates and also lacked an independent /z/ phoneme, but did already have [z] as a regular allophone of /s/ before voiced stops, as e.g. in Λέσβος [lézbos].

Later in the 4th century, ζ apparently began to represent [z], as evidenced by its being used to represent Persian z and occasional confusions between ζ and σ in inscriptions. When Aristotle said that some people would analyse ζ as σ + δ but others consider it a separate sound that does not comprise already recognised elements, he may have been referring to the start of this process. It's usually held [z] would more naturally develop out of [dz] than out of [zd], so it's been suggested this development is not a normal phonetic development but a dialectical replacement from the Koine (just as σσ replaced ττ). After short vowels at least the original quantitative pattern is likely to have been preserved by gemination, i.e. [zz]; this is also indicated by its representation as ss in the early Latin borrowing massa < Greek μάζα.