If the Sabbath were written on our hearts wouldn't we know it and seek to keep it like the Israelites were commanded?
In Jeremiah 31:33, the New Covenant involves God putting the Torah in our minds and writing it on our hearts, and in Ezekiel 36:26-27, it involves God taking away our hearts of stone, giving us hearts of flesh, and sending His Spirit to lead us in obedience to the Torah, so those who do not want to obey the Torah also do not want to be under the New Covenant.
Concerning Matt 5, Jesus explained that the law would remain until all He came to do was done. I believe Jesus did everything He came to do.
While Jesus certainly accomplished much through his first coming, there is still the second coming left to be accomplished.
It was in accordance with God's righteousness to be a doer of charity before God made the Mosaic Covenant, so that covenant becoming obsolete does not mean that it is no longer in accordance with God's righteousness to be a doer of charity. While God's covenants include instructions for how to be a doer of His righteousness, the way to do that is based on God's righteousness, not on any particular covenant. God's righteousness is eternal (Psalms 119:142), therefore any instructions that He has ever given for how to be a doer of His righteousness are eternally and cumulatively valid (Psalms 119:160). If God were to give two people different sets of instructions for how to be a doer of His righteousness in different situations, then all of those instructions would have the same trait in common, and all of them would be eternally and cumulatively valid for a third person whose goal is to know God by being a doer of His righteousness even though God did not directly give them any instructions. The only way that eternal instructions for how to be a doer of God's righteousness can be ended would be by first ending God's eternal righteousness, and the same is true for God's other character traits.
Paul wrote in 2 Cor3 KJV that the ten Commandments were done away. His take on the subject is that the ten were instructions for those under the Sinai Covenant. We are under the New Covenant and the Holy Spirit is our guide. Read 2 Cor3:6-11.
6 Who also hath made us able ministers of the new testament; not of the letter, but of the spirit: for the letter killeth, but the spirit giveth life.
God has not commanded anything that is not in accordance with walking in the Spirit, but rather Jesus set a perfect example for us to follow of how to walk in the Spirit by walking in sinless obedience to the Torah. In Acts 5:32, the Spirit has been given to those who obey God. In John 16:13, the Spirit has the role of leading us in truth, in Ezekiel 36:26-27, the Spirit has the role of leading to obey the Torah, and in Psalms 119:142, the Torah is truth. In John 16:8, the Spirit has the role of convicting us of sin, and in Romans 3:20, it is by the Torah that we have knowledge of what sin is. 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 of God who refuse to submit to the Torah. In Galatians 5:16-23, Paul contrasted with desires of the flesh with the desires of the Spirit and everything that he listed as works of the flesh that are against the Spirit are also against the Torah while all of the fruits of the Spirit are aspects of God's character that the Torah was given in order to teach us how to embody. For example, love is one of the fruits of the Spirit and the greatest two commandments of the Torah are to love God and our neighbor. Romans 2:25-29, the way to recognize that a Gentile has a circumcised heart is by observing their obedience to the Torah, which is the same way to tell for a Jew (Deuteronomy 30:6), and circumcision of the heart is a matter of the Spirit, which is in contrast with Acts 7:51-53, where those who have uncircumcised hearts resist the Spirit and do not obey the Torah.
In Romans 10:5-8, Paul referred to Deuteronomy 30 as the word of faith that we proclaim in regard to proclaiming that the Torah is not too difficult for us to obey and that obedience to it brings life and a blessing while disobedience brings death and a curse, so choose life! In Deuteronomy 32:46-47, the Torah is our very life. In Proverbs 3:18, it is a Tree of Life for all who take hold of it. In Proverbs 6:23, for the commandment is a lamp and the teaching a light, and the reproofs of discipline are the way of life. In Matthew 19:17, Jesus said that the way to have eternal life is by obeying God's commandments. In Luke 10:25-28, Jesus affirmed that the way to inherit the gift of eternal life is by obeying the greatest two commandments of the Torah. In Hebrews 5:9, Jesus has becoming a source of eternal salvation for those who obey him. In Romans 2:6-7, those who persist in doing good will be given eternal life. 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 salves to God and righteousness leading to sanctification, and the goal of sanctification is eternal life in Christ, which is the gift of God, so being a doer of the Torah is God's gift of eternal life.
So 2 Corinthians 3:6 needs to be understood in light of the other verses that says that the New Covenant involves following the Torah, that the Spirit has the role of leading us to obey the Torah, and that being a doer of the Torah is the gift of eternal life rather than a way that contradicts them. If the letter referred to correctly doing what God has commanded and that leads to death, then that would mean that God would be misleading us and shouldn't be trusted, but rather there is something deficient about following the letter that causes the Torah to lead to death rather than life.
7 But if the ministration of death, written and engraven in stones, was glorious, so that the children of Israel could not stedfastly behold the face of Moses for the glory of his countenance; which glory was to be done away:
8 How shall not the ministration of the spirit be rather glorious?
9 For if the ministration of condemnation be glory, much more doth the ministration of righteousness exceed in glory.
10 For even that which was made glorious had no glory in this respect, by reason of the glory that excelleth.
11 For if that which is done away was glorious, much more that which remaineth is glorious.
The fact that the Torah is a ministration of death for those who refuse to submit to it is not a very good reason to refuse to submit to it. The Torah is God's instructions for how to be a doer of His character traits and God's character traits are the fruits of the Spirt, which is why there are many verses that support that the Spirit has the role of leading us to obey it. However, someone can go through the motions of obeying the Torah while neglecting to be a doer of the character traits of God that it was given in order to teach us how to embody and thus neglect to know God and Jesus that is eternal life (John 17:3), which is the letter that letter that leads to death. For example, in Matthew 23:23, Jesus said that tithing was something that they ought to be doing while not neglecting weightier matters of the Torah of justice, mercy, and faithfulness. In Philippians 3:8, Paul had been int he same position where he had been obeying the Torah, but not while being focused on knowing Jesus, so he had been missing the whole goal of the Torah, and counted that as rubbish.
