In my opinion you are making a common argument whose innate flaw is that it attempts to place Ephesians 2:10 (For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand that we should walk in them.) before Ephesians 2:8-9 (For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, not of works, lest anyone should boast.). In Scripture, walking in the GOOD WORKS is the "fruit" that grows from the transformation wrought by our SALVATION; that is why Ephesians 2:8 is clear that it is "not of works" and precedes verse 10. That is why by Ephesians 2:10 we are already His workmanship when we walk in the good works which He prepared in advance for us to walk in. It is an error to attempt to earn a free gift by insisting on "walking in good works" while we are yet "dead in our sins".
In Titus 2:11-14, it notably does not say either that our salvation is the result of doing those works or that those works are the result of our salvation, but it describes the content of God's gift of salvation as being trained by grace to do those works. For example, honoring our parents is intrinsically the content of the gift of Jesus saving us from not honoring our parents, so this is not something that is cause and effect.
The content of a gift can itself be the experience of doing something, such as giving someone the opportunity to experience driving a Ferrari for an hour, where them doing the work of driving it has nothing to do with trying to earn the free gift as a wage. In a similar way, the content of God's gift of eternal life is the experience of knowing Him and Jesus (John 17:3) and God's law is His instructions for how to have that experience. In Exodus 33:13, Moses wanted God to be gracious to him by teaching him His way that he might know Him and Israel too, and in Matthew 7:23, Jesus said that he would tell those who are workers of lawlessness to depart from him because he never knew them, so knowing God and Jesus is the goal of the law (Romans 10:2-4).
There can be any number of reasons for obeying God's law other than for the goal of earning our salvation as a wage, such as for the goal of knowing God and Jesus, so verses that speak against that misunderstanding of the goal of the law should not be mistaken as speaking against our salvation requiring us to choose to obey God's law for a correct goal. In Ephesians 2:10, we are new creations in Christ to do good works, so while we do not earn our salvation as a wage by our works, doing good works is nevertheless intrinsically part of our salvation from not doing good works. While Paul denied in Romans 4:4-5 that we can earn our justification as a wage, he also said in Romans 2:13 that only doers of the law will be justified, so there must be reasons that our justification requires us to choose to be doers of the law other than for the incorrect goal of earning it as a wage, such as faith insofar as Romans 3:31 says that our faith upholds God's law.
Frankly, prior to Chapter 10, Romans is explicitly clear on what the purpose of the law was and our ability to follow it to please God ... Paul had already firmly rejected obedience to the Law as a path to salvation:
Paul spoke about multiple different categories of law other than the Law of God, such as works of the law and the law of sin. For example, in Romans 7:21-8:2, 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 he also contrasted the Law of the Spirit of Life with the law of sin and death, so he equated the Law of God with the Law of the Spirit of Life. After all, the Spirit is God. Furthermore, in Romans 8:4-7, Paul contrasted those who walk in the Spirit with those who have minds set on the flesh, who are enemies or God, who refuse to submit to the Law of God.
In Acts 5:32, the Spirit has been given to those who obey God, so obedience to God is part of the way to receive the Spirit, however, Galatians 3:1-2 denies that works of the law are part of the way to receive the Spirit, therefore the phrase "works of the law" does not refer to obedience to anything that God has commanded, which is why we are not justified by them. In Romans 3:27, Paul contrasted a law of works with a law of faith, so works of the law are of works, while he said in Romans 3:31 that our faith upholds God's law, so it is of faith, and a law that our faith upholds can't be referring to the same thing as the works of the law that are not of faith in Galatians 3:10-11.
- Romans 3:20-21 [NKJV] Therefore by the deeds of the law no flesh will be justified in His sight, for by the law [is] the knowledge of sin. But now the righteousness of God apart from the law is revealed, being witnessed by the Law and the Prophets,
In Romans 3:21-22, it does not say that the Law and the Prophets testify that the righteousness of God can be earned through our obedience, but rather the only way to become righteous that is testified about in the Law and the Prophets is through faith in Christ for all who believe, which is why there are many verses that speak against the misunderstanding of the goal of the law of earning our righteousness.
- Romans 4:13-16 [NKJV] For the promise that he would be the heir of the world [was] not to Abraham or to his seed through the law, but through the righteousness of faith. For if those who are of the law [are] heirs, faith is made void and the promise made of no effect, because the law brings about wrath; for where there is no law [there is] no transgression. Therefore [it is] of faith that [it might be] according to grace, so that the promise might be sure to all the seed, not only to those who are of the law, but also to those who are of the faith of Abraham, who is the father of us all
In John 8:39, Jesus said that if they were children of Abraham, then they would be doing the same works as him. In Genesis 18:19, Genesis 26:4-5, and Deuteronomy 30:16, all of the promises were made to Abraham and brought about because he walked in God's way in obedience to His law, he taught his children and those of his household to do that, and because they did that. God's law is how the children of Abraham knew how to be blessed by walking in God's way (Psalms 119:1-3), so the way to inherit the promise through faith of being a blessing to the nations is by turning the nations from their wickedness and teaching them to walk in God's way in obedience to His law, and Jesus was sent as the fulfillment of the promise to bless us by turning us from our wickedness (Acts 3:25-26). So the children of Abraham are not multiplied through physical descendants, but through teaching others to walk in God's way in obedience to His law through faith in the promise (Romans 9:6-8).
- Romans 6:14-15 [NKJV] For sin shall not have dominion over you, for you are not under law but under grace. What then? Shall we sin because we are not under law but under grace? Certainly not!
In Romans 6:14, it refers to the law that we are not under as being a law where sin had dominion over us, which does not describe the Law of God, which is a law where holiness, righteousness, and goodness have dominion over us (Romans 7:12), but rather it is the law of sin where sin had dominion over us. Furthermore, in Romans 6:15, being under grace does not mean that we are permitted to sin, and sin is the transgression of God's law (1 John 3:4), so we are still under God's law, but are not under the law of sin. In Psalms 119:29-30, David wanted to put false ways far from him, for God to be gracious to him by teaching him to obey His law, and he chose the way of faithfulness, so this has always been the only way to become righteous by grace through faith that is testified about by the Law and the Prophets, and this is what it means to be under grace.
Moreover, everything else in Romans 6 speaks in favor of obedience to God's law and against sin. For example, in Romans 6:19-23, we are no longer to present ourselves as slaves to impurity, lawlessness, and sin, but are now to present ourselves as slaves to God and to righteousness leading to sanctification, and the goal of sanctification is eternal life in Christ, which is the gift of God, so again obedience to God's law is the content of His gift of the experience of eternal life, and Romans 7 should not be interpreted in a way that is contrary to this:
- Romans 7:4-7 [NKJV] Therefore, my brethren, you also have become dead to the law through the body of Christ, that you may be married to another--to Him who was raised from the dead, that we should bear fruit to God. For when we were in the flesh, the sinful passions which were aroused by the law were at work in our members to bear fruit to death. But now we have been delivered from the law, having died to what we were held by, so that we should serve in the newness of the Spirit and not [in] the oldness of the letter. What shall we say then? [Is] the law sin? Certainly not! On the contrary, I would not have known sin except through the law. For I would not have known covetousness unless the law had said, "You shall not covet."
In Romans 7:1-3, there is no point at which the woman was set free from needing to obey any of God's laws, and if she were to get married to a second husband after the death of her first, then she would still be required to refrain from committing adultery, so there is nothing that leads to the conclusion in verses 4 that in the same way we have therefore been set free from all of the Law of God. In 1 John 2:6, those who are in Christ are obligated to walk in the same way he walked, so it doesn't even make sense to interpret Romans 7:4 as saying that we need to reject the way that Christ walked in order to become unified in him. Keep in mind that in Romans 7:22-23, Paul delighted in obeying the Law of God, but contrasted that with the law of sin that held him captive, so if Romans 7:5-6 were referring to the Law of God, then that would mean that Paul delighted in stirring up sinful passion in order to bear fruit unto death and that he delighted in being held captive, which is absurd, but rather it is the law of sin that he described as holding him captive. A law that stirs up sinful passions in order to bear fruit unto is a law that is sinful, but Romans 7:7 says that the Law of God is not sinful, but how we know what sin is, so it also can't be referring to the same law as Romans 7:5. So verses that refer to a law that is sinful, that causes sin to increase, or that inhibits our obedience to the Law of God, or that Paul did not delight in obeying should be interpreted as referring to the law of sin rather than the Law of God, such as Romans 5:20, Galatians 2:19, Galatians 5:16-18, and 1 Corinthians 15:56.
- Romans 9:31-32 [NKJV] but Israel, pursuing the law of righteousness, has not attained to the law of righteousness. Why? Because [they did] not [seek it] by faith, but as it were, by the works of the law. For they stumbled at that stumbling stone.
FAITH
not works of the law.
In Romans 9:30-10:4, the Israelites had a zeal for God, but it was not based on knowing Him, so they failed to attain righteousness because they pursued the law as through righteousness were earned through works rather than pursuing the law as through righteousness were by faith in Christ, for knowing Christ is the goal of the law for righteousness for everyone who has faith. Again, in Romans 10:5-8, this faith references Deuteronomy 30:11-16 in direct connection to Romans 10:9-10.