As I wrote in the comments, the modern Septuagint we have today is not the one made by the 72 elders. This is more so true for the Septuagints of the Prophets and Writings, which weren’t even translated by the elders:
"The Septuagint Pentateuch, which is all that is discussed [in the Letter of Aristeas], does, however, constitute an independent corpus within the Greek Bible, and it was probably first translated as a unit by a company of scholars in Alexandria about the middle of the 3rd century BCE.
The Septuagint, as the entire Greek Bible came to be called, has a long and complex history and took well over a century to be completed. It is for this reason not a unified or consistent translation." (Britannica).
I heard once somewhere that the original Septuagint may have been lost when Caesar burned down the Library of Alexandria, but I don’t think there’s any way to truly verify that claim (unless there's a source that recorded this). Some evidence to this may be found in the time of Rabbi Yehoshua and Rabbi Eliezer, who commissioned Aquilas the Ger to create a new Greek Targum (Yerushalmi Megillah 10b) – apparently because the original one could no longer be accessed in order to create exact copies. It seems that by their time, so many mistakes and subjective interpolations had been included by generations of scribes that it became necessary to start again from scratch. Prof. Shmuel Krauss in his essay "Two Hitherto Unknown Bible Versions In Greek" suggests that there may have been more than one new Jewish Greek Targum around this time, and at least one of these was created by ben-Tigla (Kohelet Rabbah 12:12).
Meanwhile, the Christians continued using the older targums, or else went about creating new ones, but did not yet see a need to create a uniform version. By the time we arrive in the early Amoraic period, there were dozens, perhaps hundreds of different Greek targums floating around with many errors and subjective interpolations (see for example Justin Martyr's claim that the Jews removed verses from the Tanach – evidence of verses added in by Christians (the verses don't make sense in context and obviously are only there to show that Jesus is in Tanach)). It was around the time of Rabban Gamliel III, son of Rebbi (who, by the way, is alluded to here), that the Church Father Origen realized that the significant differentiation between the targums was causing problems in terms of understanding the Bible within the Christian community, and so set out to create a new Septuagint, called the Hexapla:
"Despite the tradition that it was perfectly translated, there are large differences in style and usage between the Septuagint’s translation of the Torah and its translations of the later books in the Old Testament. In the 3rd century CE Origen attempted to clear up copyists’ errors that had crept into the text of the Septuagint, which by then varied widely from copy to copy, and a number of other scholars consulted the Hebrew texts in order to make the Septuagint more accurate." (Britannica).
The Hexapla consisted of six columns of text: The Hebrew, the Hebrew transliterated in Greek letters, three different Greek targums and a recension, a combined version of all of the three targums used by Origen. Unfortunately (for Christians and academic scholars), most later scribes only copied the combined version and not the earlier, uncombined versions. A later Church Father, Lucian, and a non-Christian, Hesychius, also attempted to create Septuagint recensions as well.
The sages were certainly aware of these new Septuagintal projects. Rabbi Reuven Margolies in his essay "The Sages of the Talmud and the LXX" (המקרא והמסורה, pg. 59–62) brings eight examples of places in which the sages hinted at knowledge of the new Septuagints. For example:
"In Tosefta Bava Kama 6:7: Rabbi Yossi said in the name of Rabbi Yishmael: "In the first commandments it says: "You and your son and your daughter and your ox and your donkey and all of your livestock", the ox and the donkey are included in livestock, so why were they excluded? To teach etc", yet it's interesting that before us, in the first commandments, it doesn't say "ox and donkey"; only the LXX translated based on the second commandments: βοῦς σου καὶ τὸ ὑποζύγιόν σου καὶ πᾶν κτῆνός (Your ox and your donkey and every beast)."
We find, therefore, that the Amoraim were aware of the new translations but weren’t able to pull out the original to point out the faults in the new ones. What they had was their era’s Masoretic Text and the tradition of the list of changes that the 72 elders made in the original Septuagint (note that Aquilas or any other translator didn't need to adhere to the changes made by the 72 elders because they were made due to the fact that the translation was commissioned by Ptolemy).
Fast-forward to the time of Rashi and the Tosfot: While I don’t have proof right now that Rashi didn’t have a Septuagint in front of him, it wouldn’t surprise me that he didn't have one for two reasons:
In Eruvin 65a he attributes the verse "בצר אל יורה" to "possibly ben Sira". As this verse does not exist in ben Sira, we see that he did not have ben Sira before him (and this is also understood from his phrasing of "possibly" (שמא)). Moreover, he did not go to any neighboring Christian libraries to check their copies of ben Sira. I would say that the same would have been the case with the Septuagint or any other book that was only available at the time in Greek.
I doubt Rashi knew enough Greek to be able to read the Septuagint in any case. No evidence specifically for Rashi, but there's some pieces of evidence that the Tosafists didn’t know Greek (see here), and since they came from the same school of thought and the same area of Europe, I think that the same could be said of Rashi (I'm aware Rashbam knew Latin, though).
It's important to note that although the number of differences between the modern LXXs and the MT is much more significant than those between the original LXX and the MT, and the differences in the lists are mostly not the same ones, there's at least one difference recorded in the gemara and midrashim as pertaining to the original LXX that was preserved within the new one(s) – that of the change from "hare" to "hairy-legged/rough-footed" (ואת שעירת הרגלים, spelled צעירת In some versions, see here, pg. 13, footnote 1). So while some scholars and/or Christians may be left scratching their heads about the usage of a rarer synonym for "hare" - Jews at least know the reason for this. At the same time, we have evidence that the later Septuagints still contain traces of the first one.