In Romans 3:27, Paul contrasted a law of works with a law of faith, in Galatians 3:10-12, he contrasted the Book of the Law with "works of the law", and in Romans 3:31, he said that our faith upholds the Law of God in contrast with Galatians 3:10-12 where he said that "works of the law" are not of faith, so that phrase does not refer to the Law of God, which is why it is not of faith. God is trustworthy, therefore His law is also true worthy (Psalm 19:7), so the way to trust in God is by obediently trusting in His instructions, it would be contradictory to think that we should rely on God but not on His instructions, and the position that God is a giver of untrustworthy instructions that are not faith denies the trustworthiness and faithfulness of God.
According to Deuteronomy 27-30, the way to be blessed is by relying on the Book of the Law while the way to be cursed is by not relying on it, so Galatians 3:10 should not be interpreted as Paul quoting from that passage in order to support a point that is arguing the opposite of that passage. Rather, the fact that cursed is everyone who does not continue to do everything in the Book of the Law straightforwardly means that the way to avoid being cursed is by continuing to do everything in the Book of the Law and that those who rely on "works of the law" instead thereby come under that curse. '
In Galatians 3:10-12, Paul associated a quote from Habakkuk 2:4 that the righteous shall live by faith with a quote from Leviticus 18:5 that the one who obeys the Law of God shall attain life by it, so the righteous who are living by faith are the same as those who are living in obedience to the Law of God. Moreover, the context of Habakkuk 2 does not present the righteous living by faith as being a way of living that is an alternative to living in obedience to the Law of God. In Isaiah 51:7, the righteous are those on whose heart is the Law of God, and in 1 John 3:4-7, everyone who is a doer of righteous works in obedience to the Law of God is righteous even as they are righteous, so the righteous living by faith does refer to a manner of living that is not in obedience to, but rather it is describing the manner that th righteous live in obedience to it.
In Deuteronomy 28, it describes the blessing of lawfulness and the curse of lawlessness, so Christ redeeming us from the curse of the law is redeeming us form our lawlessness so that we can be free to enjoy the blessing of becoming workers of lawfulness. In Titus 2:14, it does not say that Jesus gave himself to redeem us from the Law of Moses, but in order to redeem us from all lawlessness and to purify for himself a people of his own possession who are zealous for doing good works, so the way to believe in what he accomplished through the cross is by becoming zealous for doing good works in obedience to the Mosaic Law. Likewise, the Law of Moses is how we know how to be blessed (Psalms 119:1-3), so the way that the blessing of Abraham comes to the Gentiles is by turning Gentiles form their wickedness and by teaching the to obey the Law of Moses in accordance with spreading the Gospel message (Acts 3:25-26).