Re: "something both different and new to the Galatians"
Rather than a "new" Gospel, I see the qualitatively different Gospel as one that is outmoded.
As I read Gal 1:6-7, the syntax and meaning may be translated as follows:
"Unless there are some who are troubling [ταράσσοντες] you and wanting to corrupt the gospel of Christ, I am surprised that you are so quickly deserting him who called you in the grace of Christ for a qualitatively different [ἕτερον] gospel which does not exist anymore (ὃ οὐκ ἔστιν ἄλλο).
Per this discussion, https://www.ibiblio.org/bgreek/forum/vi ... php?t=5525 , I interpret ἄλλο as an adjective functioning adverbially ("exist anymore") in Gal 1:6-7. Also later in the book ("think otherwise") :
I am confident in the Lord that you will not think otherwise (ὅτι οὐδὲν ἄλλο φρονήσετε·). The one troubling you will bear the judgement, whoever that may be.
I read Paul describing the qualitatively different Gospel as a form of the Gospel that once existed, but does not exist anymore. It is outmoded.
Paul speaks of the transition from the outmoded Gospel to the Gospel in the "now" of the letter in Gal 2:15-16,
...We ourselves are Jews by birth, and not Gentile sinners. Nevertheless--knowing that except through the faithfulness of Jesus, a person is not justified by works of law--even we ourselves have believed in Christ Jesus that we might be justified by the faithfulness of Christ, and not by works of the Law, because all flesh will not be justified by works of the Law.
I take "all flesh" as spotlighting Gentile "flesh". The qualitatively different Gospel may have been ok for people who were already practicing Jewish "works of the law." For them the faithfulness of Christ and the works of the law might work together such that "not one jot" would be removed from the law. But for Gentiles, another Gospel was needed, one without requirement of "works of the law."
Matthew 5:17-20 is saying "except through the faithfulness of Jesus, a person is not justified out of works of law" as it were: "unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven":
17Do not think that I have come to abolish the Law or the Prophets. I have not come to abolish them, but to fulfill them. 18For I tell you truly, until heaven and earth pass away, not a single jot, not a stroke of a pen, will disappear from the Law until everything is accomplished.
19So then, whoever breaks one of the least of these commandments and teaches others to do likewise will be called least (ἐλάχιστος, cf. 1 Cor 15:9, "I am least ἐλάχιστος of the apostles") in the kingdom of heaven; but whoever practices and teaches them will be called great (μέγας) in the kingdom of heaven. 20For I tell you that unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven.
I think Matt is showing us the old Gospel (combining works of the law with following Jesus) that Paul considers outmoded--i.e. outmoded given the death of Jesus and the coming of the Spirit to uncircumcised Gentiles.