In the interests of fairness, there is a distinction that needs to be made here.
From a Christian standpoint, you are right when saying that the OT canon - along with the NT canon, of course - was fixed by the Catholic Church in the 4th and 5th Centuries. And that is all that should matter to us, since we believe that the Holy Spirit guided the process from the viewpoint that Christianity, as a fullfillment of Judaism, had supplanted it with respect to authority. However, the Jews today, obviously, do not recognize that authority of the early Church to decide anything. Their ancestors came up with the Jewish canon of Scripture on their own, at the rabbinic council of Jamnia (also known as Javneh) about 90 AD.
It is true that the two canons differ, in that the Jews adopted the Masoretic text (Hebrew) and the Christians adopted the Septuagint text (Greek). It is true, from our standpoint, that the Jewish council, coming 60 years after the founding of the Church and 20 years after the destruction of the Jerusalem Temple, no longer had the authority to canonize Scripture. And, finally, it is true that the council of Jamnia was convened in the first place largely to circumvent the growth and authority of Christianity. Nevertheless, looked at from the Jewish POV, our councils mean nothing to them, and, regardless of its motivations, Jamnia determined their canon of Scripture without our help. The Jewish canon being independently derived, they would say that they owe us "nothing." By default, they arrived at a canon that is 39/46 the same as ours; they're not about to acknowledge us in the process. On purely human terms, they would be correct in saying we had nothing to do with their Scripture.
The so-called "Council of Yavneh" is conjectural.
The city did become a center of scholarship after the destruction of the Second Temple when Rabban Yohanan ben Zakkai reestablished the Sanhedrin there. Rabban Gamaliel II attracted many of the greatest scholars of the day. Yavneh remained a center of scholarship until the Bar Kokhba revolt in the early 2nd century, CE.
The earliest evidence of a "Palestinian Canon" may be found in the final redaction of the Mishnah, around 200 CE. The Mishnah shows certain disagreements among the Jews regarding the canon, however, no canonical list is given.
Certainly the Dead Sea Scrolls evidence a wide variety of Jewish thought on the nature of the Jewish canon and inspiration in this period.
The Septuagint or Greek Jewish Canon appears about 200 BCE and remains influential on Jews in the Diaspora and Christians until the final redaction of the Mishnah, around 200 CE.
The first evidence of a complete Jewish Canon in the post-second Temple period is the Masoretic efforts which began in the 7th century CE and was not complete until the 10th century CE.
There is no evidence of a settled Jewish Canon in the post-second Temple period until the Aleppo Codex, circa 920 CE. Maimonedes used the Aleppo Codex to compile the Hilkhot Sefer Torah (Laws of the Torah Scroll) in his Mishnah Torah in which he sets down the exact rules for transcription. His halakhic ruling sets down the Aleppo Codex as the supreme textual authority for the Jewish Scriptures, in effect "closing" the Jewish canon.