The Septuagint is more accurate and has Shem dead long before Abraham.
The Masoretic texts were altered by the Rabbis after the time of Christ.
Interesting; as I said, it is controversial. Just as the Masorah was fashioned in the Christian era, there is no evidence that much of the Septuagint was also not translated in the Christian era. The Letter of Aristeas has been interpreted as a later forgery by some. German scholar Paul Kahle says The Septuagint, which originally had only the Torah, with its authorized form advocated in the Letter of Aristeas, emerged as a full version only in and for the Christian Church.
I have a copy of the Septuagint; the few times that I have sought the Greek rendering of a Hebrew word from the Masoretic text I have to say that I have been disappointed. Of course that is influenced by how I interpret the text so obviously my judgment is not objective.
It is not just the Masorah that interprets Shem as Melchizedek. Hebrew Streams, in its interpretation of Dead Sea Scroll 11Q13, mentions 'rabbinic tradition':
The Palestinian Targum (Targum of Jonathan ben Uzziel) on Genesis 14:18 says Melchizedek was “Shem the son of Noah, the king of Yerushalem.” Whether this means he was a reincarnation of Shem or the original Shem resurrected is unclear (the length of his given life would overlap that of Abraham). But the Shem/Melchizedek identification is common (BT Nedarim 32b {Babylonian Talmud}; Pirkei Rabbi Eliezer 8 and 27, 3; Midrash Numbers Rabbah 4, 8).Even Martin Luther preferred the “Shem” identification. The New Testament, however, does not support this idea.