No one's ever been able to find a writing that we know was written in Greek that matches the NT style or the things that the LXX and NT have in common that are clearly Semitic in style.
Current research seems to place your thesis in some doubt. A work on Greek aspect entitled Verbal Syntax in the Greek Pentateuch states:
"Over the last century it has become possible, in the light of the newly discovered evidence of Greek papyri coupled with methodological advances, to demonstrate more and more clearly in various respects the affinities of LXX Greek with the contemporary Koine vernacular of Egypt. This has led in large measure to a resolution of the old dispute.
The method of translation adequately explains the Hebraistic cast of the LXX. It is unnecessary to propose the existence of a special Jewish Greek dialect to explain the abnormalities. Nevertheless, the notion of Jewish Greek continues to find its advocates, especially in the broader sphere of biblical Greek studies. The present work will supply further clear evidence of ordinary Koine characteristics in the translation Greek of the LXX"(T.V. Evans, Verbal Syntax in the Greek Pentateuch: Natural Greek Usage and Hebrew Interference. Oxford: Oxford University Press, 2001, page 4).
Evans stresses what other scholars working with the ancient papyri have highlighted and emphasized for years, namely, that the LXX was evidently translated in Koine Greek and it bears many literary marks that inexorably link it with the Greek papyri of Egypt.