Paul spoke about multiple different categories of law, such as the Law of God, the law of sin, and works of the law, so you need to justify which law we should interpret Paul as referring to because you are guaranteed to misunderstand him if you assume that he was always speaking about the Law of God rather than just assuming that he was always speaking about God's law.
For example, in Romans 3:27-31, Paul contrasted a law of works with a law of faith, so works of the law are of works, while he said in 3:31 that our faith upholds the Law of God, so it is the law of faith. Christ set a sinless example of how to walk in obedience to the Law of Moses, and as his followers we are told to follow his example (1 Peter 2:21-22), so Paul's problem in Galatians was not with those who were teaching Gentiles how to obey the Law of Moses as if following Christ was somehow a negative thing, but rather his problem was with those who were wanting to require Gentiles to obey their works of the law in order to become justified.
In Romans 7:21-25, Paul said that he delighted in obeying the Law of God and served it with his mind, but contrasted that with the law of sin, which he served with his flesh, and Paul should not be interpreted being in opposition to God and as speaking against obeying a law that he delighted in obeying, so I've made the case in my previous post for why Romans 7:4-6 should be interpreted as referring to the law of sin rather than the Law of God.
Jesus did remove al the OT law at His death, Eph 2:14-15, removing the 10 commandments with His on NT law.
All of God's righteous laws are eternal (Psalms 119:160), but Ephesians 2:14-15 is referring to a law that is not eternal, therefore it is not referring to any of God's laws. God did not make any mistakes when He gave the law, so he had no need to remove His own laws. Furthermore, God did not give any laws for the purpose of creating a dividing wall of hostility, but rather God's law instructs us to love our neighbor as ourselves, so I'm not seeing any justification for interpreting those verses as referring to the Law of Moses, especially when Jesus specifically said that he came not to abolish the law (Matthew 5:17).
Matthew 5:27-28 aultery is not wrong because the 10 commandments says its wrong but because Christ says it's wrong. The OT condemned the physical act of adultery but Christ went further condemning the thoughts of lusting in the heart as much as the overt act of adultery.
The same Father who gave the law to Moses also sent Jesus, who set a sinless example for us to follow of how to walk in obedience to it, and who did not hypocritically preach something other than what he practiced, so there is no disagreement. Jesus would have still taught full obedience to the Mosaic Law by example, even if he had reiterated nothing, and as his followers we are told to follow his example (1 Peter 2:21-22), so we do not need him to have reiterated anything in order to know that we should still obey the Father. The command not to look at a woman with lust in our hearts is just the correct application of the 7th and 10th Commandments against adultery and against coveting in our hearts, so Jesus was not teaching anything brand new in disagreement with the Father. In Deuteronomy 4:2, it is a sin to add to or subtract from the Mosaic Law, so Jesus did not do that.
1 Corintinas 9:21 Paul was under Christ's NT law not under the law of Moses.
In 1 Corinthians 9:21, Paul said in a parallel statement that he was not outside the Law of God, but under the Law of Christ, so he equated the Law of God with the Law of Christ, and the Law of Moses is the Law of God, so he was affirming that he was under the Law of Moses. God is not in disagreement with Himself about which laws we should follow, so the Law of Christ is the same as the Law of the Spirit and the Law of the Father, which was given to Moses. Christ spent his ministry teaching how to obey the Law of Moses by word and by example, so it wouldn't make sense to think that the Law of Christ was something other than what Christ taught.
Romans 7:1-6 Paul condemned going back to the OT law and keeping it as he condemned those in Galatian who had left the NT gospel (Galatians 1:6-7) going back to the OT law.
Jesus began his ministry with the Gospel message to repent for the Kingdom of God is at hand, and the Mosaic Law was how his audience knew what sin is, so repenting from our disobedience to it is an integral part of the Gospel message, which he prophesied would be proclaimed to all nations (Matthew 24:12-14). In Romans 15:4, Paul said that OT Scripture was written for our instruction and in 15:18-19, his Gospel message involved bringing Gentiles to obedience in word and in deed, so his Gospel was on the same page in regard to teaching repentance from our sins.
Galatians 2:21 if the OT law could make one right with God, then Christ died in vain. Yet the OT law could not make one right before God (Hebrews 10:1-4). The OT law was a 'yoke of bondage' Galatians 5:21 for it could not free one from sin. Those Galatians who left the NT left the freedom the NT brings in Christ and returned to the yolk of bondage of the OT which required perfect, flawless law keeping of the whole law (Galatians 5:3). Jst one sin would bring the curse of the OT law upon one (Galatians 3:10). Since the Jew could not keep the OT law perfectly therefore cuold not be justified by that hence Paul says 'no man is justified by the law in the sight of God', (Galatians 3:11). Therefore for the Christian to leave the NT and go back to the OT law looking for justication is sinful (Romans 7:1-6) but also the OT law requires perfect, flawless law keeping to the WHOLE law (not just the 10 commandments) else one brings the curse of that OT law upon himself. What the Christian does, he must find justification for it in the NT.
We do not earn our righteousness by obeying God's law because it was never given for that reason, but that doesn't mean that we don't need to obey it for the purposes for which it was given. Even if someone managed to live in perfect obedience to the Mosaic Law, they still would not earn their justification because our justification is not something that can be earned as a wage (Romans 4:4-5). Trying to earn our justification has always been a fundamental misunderstanding of why we should obey the Law of Moses.
The reason why God saved the Israelites out of bondage in Egypt was not in order to put them under bondage to His law, but rather it is for freedom that God sets us free (Galatians 5:1), and God's law is a law of freedom (Psalms 119:45). In Psalms 119:142, God's law is truth, and in John 8:31-36, it is sin in transgression of God's law that puts us in bondage, while it is the truth that sets us free. In Titus 2:14, Jesus gave himself to redeem us from all lawlessness and to purify for himself a people who are zealous for doing good works, so the freedom that we have in Christ is the freedom from sin, not the freedom to sin.
In Galatians 3:10-12, Paul associated a quote from Habakkuk 2:4 with a quote from Leviticus 18:5, so the righteous who are living by faith are the same as those who are living in obedience to the Law of Moses, while no one is justified before God by works of the law because they are not of faith, unlike the Law of Moses. In Isaiah 51:7, the righteous are those on whose heart is the Law of Moses, so the righteous living by faith does not refer to a manner of living that is not in obedience to it.