perhaps not an answer but rather a comment - I just found my notes, based on Woodard 2010/2014.
Adaptation: Greek-Phoenician bilingual speakers (scribes or mercenaries literate in the syllabic Cypriot orthographic tradition), “proceeding with intentionality and arbitrariness” (p. 35).
Consonant clusters with /s/ in Phoenician: three affricates, /dz/ (grapheme: zayin), /ts/ (grapheme: samek), /ts’/ (grapheme: sade).
Consonant clusters with /s/ in Ancient Greek:
The Cypriot syllabary: V, CV are allowed, two CCV (ksa, kse).
“It would appear that the value of zeta is somewhat schizophrenic” (Woodard 1997: 162).
*zd > dz happened prior to the alphabetic period (see p. 162 for evidence)
In literary Lesbian (Sappho, Alcaeus) zeta is used for *dy; sigma+delta is used for zd.
Woodward 1997: 187"
“The Phoenician character zayin was utilized by the Greek adapters to represent the sound sequence [zd] (the sound of zeta). Syllabic characters with the consonantal value [zd-] existed in the Cypriot script (probably ultimately a feature inherited from the Mycenaean syllabary); consequently, provision was made by these Cypriot adapters for expressing such a sequence with an alphabetic symbol. Semitic zayin represented a voiced fricative [z], but in Cypriot Phoenician this sound appears to have been some sort of "double consonant," thus rendering zayin particularly suggestive for representing the Greek sequence [zd]. Without positing such a syllabic Cypriot background for the alphabetic character zeta, the use of a single alphabetic symbol to represent [z] + [d] (the value consistent with linguistic evidence) is enigmatic.”