The Hebrew “canon†aimed to exclude “Christian†writings, which would include many Jewish apocalyptic writings, and many wisdom writings in the Septuigent.
You are correct in part. Christians found ready the Greek LXX for the gentile world. A summary can be found here.
The books of the Apocrypha were not included in the Hebrew Bible, nor were they regarded as canonical by the leaders of official Judaism anywhere. Even Jews who wrote in Greek at the beginning of our era, like Philo and Josephus, recognized only the Canon of the Hebrew Bible, although they used the ‘Septuagint’ translation.. .
Our Lord and the apostles certainly did not regard the apocryphal books as part of Holy Scripture; the evidence is that they acknowledged as canonical only the books of the Hebrew Bible.
This is also comfirmed in part by a statement from the Apocryphal book of 2d Esdras, written in A.D. 100, showing that the twenty-four books of the Hebrew canon had been considered authoritative for a long time.
Regarding the effort to separate from Christianity and the LXX, there may have been components later but that didn't really pan out for quite a while later.