Once upon a time, long ago and far away, when teaching myself modern Greek (I was going to Greece to spend my very first holiday as a newly baked teacher with a regular income) I became curious about the difference in pronunciation between ancient and modern. And, in both the French and German sources I consulted was told that  ζ  was pronounced dzêta. Which made sense. The Germans still pronounce the letter Z as "ts". And since they have a tendency to invert soft and hard sounds:
"dzoo" becomes "tsoo". Logical!
I now am told that dzêta is supposed to have been pronounced sdêta. And for a while I accepted this and actually pronounced Dzeus as Sdeus. On the evidence of  Ἀθήναζε. Apparently pronounced Athênasde on the pattern of  οἴκαδε.  
Well, I quickly stopped believing that.
On principle I only believe what I can see, hear, smell or else find logical. And for me, as long as no-one comes up with better proof to the contrary, sdêta is illogical for many reasons:

• There are special letters for ks
  There are special letters for ps
  Why should there be one for sd rather than dz? Especially when there are lots of words including the  στ  letter combination:
  τοὺσδε τοὺς λόγους σκόπει· ἀγωνιστής, δικαστής, στενάζει καὶ τὰ λοιπά
  examine the following words: prize-fighter, judge, he groans etc.
  But there is no  τσ  or  δσ  combination to be found. Why not?
  As for τούσδε, quite correctly spelt σδ and not ζ (since the σ and the δ belong to different syllables), it just corroborates the fact that Athenasde would have been spelt σδ. For exactly the same reason: the σ at the end of one syllable, the δ beginning the next.
   
  
• In everyday speech letters get dropped. Hardly ever 2nd letters, always either first or last. So why did the "d", coming second, disappear?
  We pronounce
  1. xylophone as zilofone (we dropped the 1st letter k sound)
  2. psychic as saikik (we dropped the 1st letter p sound)
  3. sdoo as zoo (did we REALLY drop the 2nd letter d sound?)
  It doesn't make sense!
  I said hardly ever, because I do believe that the 2nd letter z was dropped in:
           μὰ τὸν Δία  
           τῷ Διὶ θύομεν  
           ὁ τοῦ Διὸς κεραυνός  
  Why? Try saying them fast and you'll see: in my opinion Sdií would have stayed Sdií whereas Dzií lends itself to become Dií.
   
  
• Now to the  Ἀθήναζε  proof. Why stop accepting that as proof? Since we have οἴκαδε 'homewards bound'. Fine.
  So what about ἐκεῖσε 'to there, bound for there'?
  Obviously there is no hard and fast rule that states: "bound for" is  δε  appended to the location.
  To my mind we use  δε  as long as there is no confusion (in oral communication) possible between: "bound towards" and "as for, and, but, on the other hand".
       ἐκεῖσε πορεύομαι· ἐκεῖ  δὲ οἰκεῖ ὁ φίλος μου.
  On a map:
       Χαλκίδα μὲν οὐχ εὑρίσκω, Ἀθήνας δὲ βλέπω.
  Now try this:  Ἀθήναζε δὲ ἐπανιέναι ἐθέλω  
       Do you really want to pronounce it: Athenasde de?

So, unless Dikaiopolis comes back and tells me otherwise, I shall pronounce ζ dzêta. But I let everybody else pronounce it any way they like. Because that is their good right.