At the end of the day historical testimony is toward the Deuteros not being part of after the 1st century LXX, nor part of the most authoritative canon, with the two being related, and with Christ reference to the tripartite canon in Lk. 24:44 (and as "all Scripture" in v. 27) being that one.
Thus the reason there are no complete codices that are missing the Deuteros is because the earliest complete codices are hundreds of years after 132 B.C. and the 1st century LXX, and some Christian are known to have messed with it. Yet even then the codices conflict with each other and with Trent on the issue of the contents.
Also, seeing as the last books of the Deuteros are thought to have been written some time around 100 BC (or later) while the translation of the Septuagint itself was completed by 132 BC then it leaves little time for the establishment of them as Scripture proper.
The question also arises, if the Deuterocanonical books were only added by the Christians in the 4th century to an earlier received Old Testament without them, who added them and why does the manuscript evidence only show their inclusion?
Look at your question. The answer to the last sentence is in the first one. "Christians" added them which is why the manuscript evidence from hundreds of years later show them, while the Palestinian Hebrew canon, which what Christ only quoted from, did not. To suppose otherwise is more wish than substance.
At the end of the day historical testimony is toward the Deuteros not being part of after the 1st century LXX, nor part of the most authoritative canon.
The case for a closed canon which excluded the Deuterocanonical books, and which was received universally by all the Jews, is not as strong as you would present. First, even in Palestine there was not a unanimity concerning the canon. While the Pharisees accepted what is now the Masoretic canon, the Sadducees did not. They only accepted the first five books of the Torah. The present Masoretic canon probably did not reach its current form until the 2nd century. According to Lawrence H. Schiffman, Vice Provost for Undergraduate Education at Yeshiva University:
While virtually all the Writings were regarded as canonical by the time of the destruction of the Temple in 70 C.E., arguments continued regarding the status of Proverbs, Song of Songs, Ecclesiastes, and Esther, and these disputes are attested in rabbinic literature. Second Temple literature indicates that a collection of Writings existed as early as the second century B.C.E. but was not regarded as formally closedOne piece of evidence is that the Kaige Recension, a Greek copy of Scripture that was produced by the Pharisees in the first century B.C., contains Baruch and the additions of Daniel. Additionally evidence is the fact that Rabbi Akiba de Joseph, the head of the rabbinical school in Jamnia in the 2nd century, did not just list what was in the canon, but felt that it was necessary to explicitly exclude the Deuterocanonical books. This he would not have had to do unless there were some Jews who did think that they were canonical.
The idea of two separate canons, a longer Alexandrian one and a shorter Palestinian one, was originally proposed by Protestant scholars in the 18th century to explain why Christians and Jews held two separate canons. While A.C. Sundberg has disputed this theory, his conclusion did not lead to a single Jewish canon along the lines of the Palestinian one. Rather, he posited that the canon of the Writings was not yet closed, and that the Septuagint, along with some of the Deuterocanonical books were used even in Palestine.
That being said, the idea of two canons is again gaining popularity. See Ph. Guilluame, "New Light on the Nebiim form Alexandria: A Chronography to Replace the Deuteronomistic History," The Journal of Hebrew Scripture, Volume 5, Article 9. Evidence to support the idea of an established Alexandrian canon which contains the Deuterocanonical books comes from the fact that the biblical canon of the Ethiopian Jews contains the Deuterocanonical books to this day.
Look at your question. The answer to the last sentence is in the first one. "Christians" added them which is why the manuscript evidence from hundreds of years later show them, while the Palestinian Hebrew canon, which what Christ only quoted from, did not.
Even if we were to agree that there was a single canon among the Jews that excluded the Deuterocanonical books, you yourself admit that they were added by the early Christians. The acceptance of these books was already well enough established by the 4th century that the manuscript history shows their inclusion. Guided by the Holy Spirit, this they would be free to do just as much as accept the books of the New Testament as Scripture. As for the oft made claim that there are no references to the Deuterocanonical books in the New Testament, I would suggest that you take a look at this.