The Law was given to people that God had already declared righteous by faith as instructions for how to therefore do what is righteous, so the Law is not God's instructions for how to become righteous, but how to do what is righteous. For example, helping the poor is part of God's instructions for how to do what is righteous in accordance with His righteousness, so it is something that someone who is righteous is called to do by faith, but no amount of helping the poor will cause someone who is not righteous to become righteous. Yet what your response amounts to saying that because we can't become righteous by helping the poor, therefore we can't rely on God's instructions to help the poor as a way to live righteous lives. According to Psalms 19:7, the decrees of God are trustworthy, but if you do not that we can rely on them, then does that not show a distinct lack of faith in Him?
In 1 John 3:4-10, it says that everyone who makes a practice of sinning also practices Lawlessness, that sin is Lawlessness, that no one who is born of God continues to make a practice of sinning because they are born of God, and that whoever does not practice righteousness is not born of God. So we are to follow God's instructions in His Law for how to practice righteousness and how to avoid sin, not in order to become righteous, but because we are children of God. In 2 Timothy 3:16-17, we are told that all OT Scripture (which primarily includes God's Law) is profitable for training in righteousness and equipping us to do every good work. In Titus 2:11-14, our salvation involves being trained by grace to do what is godly, righteous, and good and to renounce doing what is ungodly, sinful, and Lawless. In Ephesians 2:8-10, it says that we have been saved by grace through faith not by doing good works, but for the purpose of doing them, so following God's instruction in His Law for how to do good works is not something we are do in order to become saved, but because we have been saved. So it goes more like this.
P1- God's Law is His instructions for how to practice righteousness
P2- God's Law is His instructions for how to love Him and our neighbor
P3- We are told to practice righteousness
P4- We are told to love God and our neighbor
P5- We have faith in God to guide us in how to live righteously
P6- We love God and our neighbor
C- Therefore we should at least follow God's Law
All of the commands in the NT are based off of principles found in the OT, so there are no instructions found in the NT for how to practice righteous that are distinct from the OT, but even if additional laws for how to act according to God's righteousness were added in the NT (in violation of Deuteronomy 4:2), then way to practice would still nevertheless be inclusive of the instructions found in God's Law.
I do not consider the laws in the NT to be distinct from those of the OT, but clearly, if you consider a set of laws to be a bondage, then that reflects rather negatively on your opinion of the lawgiver and on whether they can be trusted to give good laws. God said that what He commanded was for His people's own good, to teach us how to live in a way where we will prosper and be blessed, to be a delight, and that they are not too difficult for us, so consider His Law to be bondage also shows a distinct lack of faith in Him to guide you in how to rightly live.
Again, it is important to correctly distinguish between what is said about man's works of law and about God's Law. There is no definitive article in the Greek, so the phrase "works of the law" is literally translated as "works of law", which means that it does not refer to a definitive set of laws, such as the Mosaic Law, but rather Paul used it to refer to a large body of Jewish oral laws, traditions, rulings, and fences which the Pharisees were teaching that people needed to obey in order to become saved, which is confirmed by its the use of the phrase in Qumran Text 4QMMT. This is why Paul was arguing against being saved by their works of law and in favor of becoming saved by faith, which is the one and only way that there has ever been to become saved, and by the same faith we are to uphold God's Law (Romans 3:31). In Romans 3:27, Paul was very clearly contrasting a law that was not of faith with a different law that is of faith, so man-made works of law are not of faith, while God's Law is of faith, and it straightforwardly is in regard to having faith in Him to guide us in how to rightly live.
As Jesus said in Matthew 23:23, faith is one of the weightier matters of the Law, so the Book of the Law again is of faith and those who were instead relying of their works of the law were under a curse because they were not living by faith in God and thus failing to do everything in the Book of the Law.
According to Galatians 6:2, bearing one another's burdens fulfills the requirements of the Law of Christ, so does that mean that doing so brings the Law of Christ to an end? According to Romans 15:18-19, Paul fulfilled the Gospel, so did he bring it to an end? According to Galatians 5:14, loving your neighbor fulfills the entire law, so fulfilling the entire law is something that everyone since Moses who has loved their neighbor has done, which means it does not refer to something unique that Jesus did. Rather:
Pleroo: to fulfil, i.e. to cause God's will (as made known in the law) to be obeyed as it should be, and God's promises (given through the prophets) to receive fulfilment
In Matthew 5, after Jesus said he came to fulfills the Law, he then proceeded to fulfill it six times by causing God's will (as made known in the Law) to be obeyed as it should be. According to Titus 2:14, Jesus gave himself to redeem us from all Lawlessness and to purify for himself a people of his own possession who are zealous for doing good works, and God's Law is His instructions for how to do good works, so we should not return to the Lawlessness that he gave himself to redeem us from.
Again, I have never suggested that we can become justified either by obeying God's Law or by obeying man's works of law. God had many reasons for hiving His Law, but providing the means of becoming justified was never one of them.
Those who return to their works of law in order to become saved after they have already been saved would indeed be making Christ's offering of no value, but so would returning to the Lawlessness that he gave himself to redeem us from. So I agree that we have received grace apart from our works of law, but David being taught to obey God's Law is how he received grace (Psalms 119:29), and we also have received grace to bring about the obedience that faith requires (Romans 1:5).
In Romans 10:5-10, it quotes Deuteronomy 30:11-14 in regard to what our faith says in regard the righteousness of the Law that Moses wrote about. Our faith says that God's laws are not too difficult for us, it is not far off, but is near you, in your mouth and in your heart so that you can do it. This is what it means to submit to Jesus as Lord and to submit to his commands by faith. This is how the Israelites lived or did not live by faith and the example of how we are to live or not live by faith, and we are to learn from their example of disobedience that we might not desire evil as they did, not so that we can emulate it (1 Corinthians 10:1-13). Every example of saving faith in Hebrews 11 is also an example of someone living in obedience to God's commands, so living by faith has never referred to some other manner of living that is not seeking to live in obedience to God's commands. God said that what He commanded is for His people's own good (Deuteronomy 6:24), so you can either have faith that what God said is true and therefore accordingly or you can believe that He is an unloving Father who puts unbearable burdens on His children and therefore act accordingly.
I don't see any reasons to think that they are not synonymous, so feel free to point out ways that they are not. The Law instructs us how to live according to God's righteousness and the Spirit has the role of leading us in obedience to the law (Ezekiel 36:26-27), the Father was not acting against His Spirit when He gave the Law to Moses, and the Spirit and the Son are not in disagreement with the Father about what conduct we should have. Rather the fruits of the Spirit are all in accordance with the Law and Jesus said that his teachings were not his own, but that of the Father (John 7:16), so neither the Spirit nor the Son will teach to disobey what the Father has commanded.