I'd like to hear more about this aspect from those of you who have deeper knowledge of the Septuagint. Can you describe this cutting-edge work, and what we should be learning from it? Can you tell me about Lee, Joosten, and Aitken?...the most conspicuous and least understood factor in scholarly accounts of the “language” of the NT is the Septuagint, and by extension the under-studied corpus of nonliterary Koine Greek. Although many will point to the NT authors’ familiarity with the Greek OT per se, few will account for the massive socio-religious influence that it was on balance with the natural linguistic developments that it preserves. It is in the current scholarly discussion of the Greek of the LXX that one finds so much helpful material on the development and nature of the Koine in general. There is cutting-edge work going on here (e.g., Lee, Joosten, Aitken) that needs to be related to study of the Greek of the NT in the future.
By the way, here is an excerpt of the Gleaves book Did Jesus Speak Greek? The Emerging Evidence of Greek Dominance in First-Century Palestine.