I am not well acquainted with the subject, and it is difficult to discuss some of these aspects based on an English translation of Josephus.

Josephus used the Hebrew Scripture as his major source, for this is both common sense and the most veritable source for presenting the history of the Jews.

He said that he was writing a history, "as interpreted out of the Hebrew Scriptures". This indicates that he was using a classical style of historical narrative to convey information that he was taking from the Scriptures. He was not aiming at a translation of the Scripture, but making an interpretation of facts for which the Scripture was his major source.

He then spoke of his earlier work concerning the late war with the Romans, And indeed I did formerly intend, when I wrote of the war, to explain who the Jews originally were, but he found that he should write of the recent events only and publish them, and then, at length, produce a greater work encompassing a wider scope of history, that is, the Antiquities: but because this work would take up a great compass, I separated it into a set treatise by itself, with a beginning of its own, and its own conclusion; but in process of time, as usually happens to such as undertake great things, I grew weary and went on slowly, it being a large subject, and a difficult thing to translate our history into a foreign, and to us unaccustomed language.

When he spoke about it being a difficult thing to translate our history into a foreign, he was talking about the classical style of historical narrative, as being difficult to render or present the comprehensive narrative, for which the source and interpretations were being taken from the Hebrew Scripture. This in itself has nothing to do with translation of the Scripture, but is referring to the narrative form.

Furthermore, when he spoke of translating our history into a foreign, and to us unaccustomed language, this statement does not in itself deny that the LXX containing the entire OT was present. Why would Josephus call Greek foreign or unaccustomed when we know that just before that time the Jews in the New Testament were commonly speaking and writing in Greek? Therefore, the foreignness and the unaccustomedness must really mean the style of writing and that classical style or Greek was secondary in comparison with the original expression (primarily in Hebrew) of Jewish thought.

Josephus was not speaking about how he had begun to translate the Old Testament into Greek when he first began writing, but that he found that the project of giving the history of the Jews in the form of a comprehensive classical narrative a long thing to do. Thus, he published his narrative on the late Roman War first, and only after time and labour did he present his full interpretation of Jewish history. He indicates that his source was the Hebrew Scripture for this, but this does not deny the LXX either existing (since Josephus clearly gave a historical account that indicated that the LXX did exist), nor does it preclude that Josephus did not use or refer to the LXX.

Most importantly, Hebrew Scripture may not in fact refer to the LANGUAGE, i.e. Hebraic, but to the ownership, that is, Israelite, thus, when he said Hebrew Scripture he may well, and in line with his history of the LXX, be referring either in part in the main to the LXX.

Finally historically, because Josephus wrote of the LXX as fact in Book XII chapter 2, it would be consistent if Josephus were using the LXX without specific present reference because it was understood to be the common representation of the Hebrew Scripture: otherwise he would have made some specific indication that this was not so. This is like a KJBO person speaking about the Word of God while teaching when it is understood to mean the King James Bible even if they do not specifically express it.