The similarity of the Septuagint to some Hebrew Dead Sea scrolls suggests that there was a Hebrew text type that the Septuagint was translated from, and that was not the Masoretic text type. One can argue that this Hebrew vorlage may be inferior to the Masoretic but that is another issue; the point is we have a competing text that must be interacted with.
Different books were likely translated by different scholars. So one cannot treat the Septuagint as a whole. I understand that much more attention was paid in translating the Pentateuch than the other books. Therefore it may be potentially legitimate to claim the the Septuagint's Pentateuch vorlage is closer to the original than the Masoretic, while arguing for the Masoretic with other books.
New Testament quotes of the Old Testament do not always conform to the Masoretic. Some quote the Masoretic, some the Septuagint. Horn states,
I am quite sure that Matthew quoted from a Hebrew text that agreed with the Vorlage that the Greek translators used.Other options for the New Testament authors could include: a different source text, the source texts are similar enough at the passage to preclude identification, or the quote is a paraphrase. The authors of the New Testament would have been aware of Hebrew variants and the Greek translation had been used in some synagogues.
An aside, I have no concerns with the New Testament authors being free in their Old Testament quotes. If what they write has the same meaning as the original—in terms of the point they are drawing from it—then the quote is accurate. If, however, the point is only apparent in the variant and the variant is not original this becomes more difficult to justify. This is because the reason for quoting the Old Testament is its authoritative nature. It is similar to Christians defending the trinity from 1 John 5. The trinity can be defended from Scripture but not based on this verse if it is not original. (One may be able to show the early churches' views based on the insertion of this verse though).
Josephus (and others) don't use the Masoretic. Given that Josephus' ages of the ante- and postdiluvian patriarchs parallel the Septuagint (and these are most likely to have been changed in translation) he is likely quoting the Septuagint not a Hebrew variant, so this does not add further evidence. I vaguely recall that Josephus at times uses a text that is not comparable to Septuagint which may suggest a further text, or at least a variant Septuagint type.
A further issue of much importance is that while we can take confidence in the accuracy of the transmission of the Masoretic text, this does not automatically carry over to the origin of the Masoretic text. The proverbial weakest link in a chain. If the Masoretic endeavour began after the resurrection there could be ulterior motives of the scribes given the antagonism of many Jews to the new Christian sect. This could be as sinister as removing or changing a text, one that Christians interpreted favourably in their defence of Jesus' Messiahhood; or it could be by merely favouring a text type that provided less apologetic power to the Christians. This may not seem in line with what we know of the Masoretes. However selecting a text is not the same as fastidiously transmitting it over the centuries.
Those involved in recovering the original text of the Old Testament undoubtedly know all this and more. There may be other compelling reasons to favour the Masoretic text. But I think the pendulum needs to swing back a little and we need to give more credence to the Septuagint, at least parts of it, as did some of the church fathers. There are likely groups involved in trying to recreate the original Septuagint. If it was translated over time there may have been more than one early translation of the same passage.
Resolving the Hebrew the Septuagint translators used is possible (to a degree) and this is compared with the Masoretic text. I think we need to be prepared to weight some books of the Septuagint heavier than currently.
As it is currently, in some passages the Septuagint is thought to represent the original over the Masoretic. But we need to shift this bias. If we acknowledge the Septuagint is usable when the the Masoretic is clearly wrong, then it is obvious that the Septuagint is a preferable text some of the time. This means that it may be a preferable text in other places where the Masoretic is not clearly wrong but appears inferior. Then we go from the assumption that the Masoretic is reliable unless proven otherwise to the Masoretic is one among several competing witnesses.