Aeolic θᾶς "until"

This is an RTFM question, and someone must have already worked out the answer to it; but that someone didn't work out the answer to the question in the 19th century, which would have let me look up the answer easily online. I'm actually halfway hoping that a reader will find the answer in their library, and let me know of the writeup.

The question is, what does θᾶς mean in Alcaeus, and why.

It's a tiny word of Aeolic. (At least, I think it's Aeolic.) The tinier the word, the more difficult it is to work out what it means. And θᾶς is not a word that turns up in the documents available in the 19th century: it isn't mentioned in the Ancient grammarians, or the fragments of Alcaeus known at the time. The word turns up in two fragments dug up at Oxyrhynchus:

• κῆνος δὲ παώθεις Ἀτρεΐδα[.].[
  δαπτέτω πόλιν ὠς καὶ πεδὰ Μυρσί̣[λ]ω̣[
  θᾶς κ’ ἄμμε βόλλητ’ Ἄρευς ἐπιτ.ύχε..[
  τρόπην· ἐκ δὲ χόλω τῶδε λαθοίμεθ..[·
  But let him, kinsman by marriage to the Atreidai,
  keep on devouring the city just as he did with Myrsilos,
  until such time as Ares chooses to turn us
  to our weapons. This present anger may we put from our minds... (Page & Lobel fr. 70 lines 6–9; translation from A.M. Miller)
  
• ...]ξηι δὲ θᾶς̣ κε Ζεῦς̣ [ "... until Zeus..." (Page & Lobel fr. 206 line 6)

Now, the translators know what θᾶς means: both the Loeb and the Miller render it as "until". Someone somewhere would have published how they worked out that θᾶς means "until". But without finding it anywhere obvious online, I don't have a citation for how they know what it means.

I can guess, which is why I have a blog.

• θᾶς has a circumflex, which implies a contraction—i.e. that it goes back to something in proto-Greek like *tʰaos or *tʰaes
  
• Attic Greek has a word for "until", which is ἕως /héɔːs/. That looks like it could be related.
  
• Attic εω always makes you think of quantitative metathesis—that is, it should correspond to Ionic ηο, and proto-Greek, Doric and Aeolic *ᾱο.
  
• Doric *ᾱο would have contracted to ᾱ, and would have taken a circumflex as a contract
  
• And indeed, Attic ἕως /héɔːs/ corresponds to Epic ἧος, εἵως /hɛ̂ːos, héːos/, Doric ἇς /hâːs/, and Aeolic ἆς /âːs/, all meaning "until".
  
• So an Aeolic θᾶς ends the same way as the Aeolic for "until".
  
• But why is there an initial /tʰ/?
  
• If proto-Greek had something like *ἇος /hâːos/, and we're trying to explain /tʰâːs/, the simplest explanation is /t + hâːos/. We already see /t/ prefixed to a lot of Greek pronouns and adverbs, as a demonstrative: ὅτε "when" > τότε "then", οἷος "of which sort" > τοῖος "of that sort", etc.
  
• /t/ does get prefixed to ἕως, as a correlative counterpart to it: Attic τέως "in the meantime; for a while; (rarely) until".
  
• The prefix also turns up in other dialects: Epic τείως (from εἵως), though the reading τῆος (from ἧος) has been metrically reconstructed in Homer.
  
• Hesychius records Cretan τάως /táɔːs/ as meaning τέως. Cretan is an Archaic Doric dialect, and we would expect a proto-Doric /t + hâːos/ > */tâːos/; Kühner-Blass reports that Nauck thought the original Cretan form was indeed τᾶος, and somewhere along the line the word was respelled to match the ending of Attic τέως.

So we have an answer, right? θᾶς is derived from /t + hâːos/, like τέως is.

The problem is, none of the correlatives have /tʰ/ in them: the Doric is τάως, not *θάως, just as ὅτε goes to τότε, not *θότε. And even if correlatives did have /tʰ/, the last dialect you'd expect to find an initial breathing is Alcaeus' Aeolic, which systematically dropped its initial rough breathing (psilotic): remember that "until" in Aeolic is ἆς /âːs/, not ἇς /hâːs/.

So the derivation doesn't make sense for Aeolic, or indeed for proto-Greek; "for a while" should have been *τᾶς, not θᾶς. Because of the final two letters and the circumflex, I'm reasonably sure θᾶς is somewhow related to ἆς = ἕως, and I wouldn't be flabbergasted if the θ- turns out to have been a mistake. (The papyri in Oxyrhynchus weren't personally penned by Alcaeus: they reflect a standard later edition, which we guess introduced elements from the later Aeolic of Asia Minor, and could have distorted the language in other ways.)

If it does turn out to be something completely different, well, that will be a relief...