Be careful how you use that word "Septuagint."
I have copies of what is today called the Septuagint that are like what you're describing, where all the books of the Old Testament along with the Apocrypha are bound in a single volume. But at the time of the apostles, no such book existed. All the books they used as scripture were then on separate scrolls. Some synagogues would have some scrolls, and some others (see, for example Luke 4:17). The books regarded as Scripture by the Jews of Palestine in Jesus's day, and by Jesus himself did not include the Apocrypha.
Of course, these books had all been translated into Greek. There was a tradition that the Pentateuch (nothing else, just the Pentateuch) had been translated by 70 (or 72) translators in Alexandria. And this is where we get the title "Septuagint" (from the Latin for 70) that would later be applied to that much longer collection. All the other books had also been translated, some of them multiple different times, by anonymous people at times and places we don't know. The New Testament was written in Greek, and so when it quotes the Old Testament, those quotes are also in Greek. This leads some to say sloppily that they are quoting "the Septuagint," which unfortunately misleads people like yourself into thinking they were quoting from a collection that included the Apocrypha. But no book of the Apocrypha is ever quoted as Scripture anywhere in the New Testament. Nor were those books regarded as Scripture by the Pharisees of Palestine, who, by all indications in the Gospels, shared the same delimitation of what is and isn't Scripture as Jesus did.
I should have made myself clearer, as it appears I may have mistakenly led you to believe that I meant the Septuagint included those books that are called apocrypha. I did not mean to do that and you are correct in pointing this out.
However, some of things you have said are indeed inaccurate.
For example, the Greek translation of the Pentatarch (the Septuiginat) was exactly the version used by the early Church and the same one mentioned 80% of the time when the Old Testament is referred to in the New Testament. This is because the Septuagint was the version most widely used and which more clearly expressed the prophecies of Christ. The version used centuries after His death, the Hebrew text used in the modern Protestant Bible, while extremely close to the Septuagint, has changed certain verses and wording to minimize the prophecies of Christ (which would be natural given that it was the Jews who compiled and translated this completed version sometime in the seventh century AD).
You make this statement "But no book of the Apocrypha is ever quoted as Scripture anywhere in the New Testament." But neither does the New Testament quote from Esther, Song of Songs and Ecclesiastes. Does this by your definition mean these books are Apocrypha?
And even more against your point, are these instances in the New Testament:
1) What Paul wrote in 1 Corinthians 2:9, preceded with the phrase “it is written”, resembles but is not equal to Isaiah 64:4. According to Ambrosiaster [13] (c. 4th century AD) it is a quotation from the apocryphal Apocalypse of Elijah.
2) Paul wrote in 1 Corinthians 10:4 about the spiritual rock that followed the Israelites during Exodus and he named two magicians who opposed Moses in 2 Timothy 3:8 – both are not found in the book of Exodus but in lost Apocryphal writings.
3) In 2 Peter 2:22, Proverbs 26:11 is placed in par with a proverb from outside the Bible.
4) Jude 9 quotes from the Apocryphal book the Ascension of Moses
5) Jude 14-16 quotes from the apocryphal book 1 Enoch 1:9.