Your assumption that the old covenant was eternal is incorrect. Thus, your reasoning was flawed. Since the old covenant no longer exists, it cannot be eternal.
In Exodus 33:13 and Leviticus 24:8, it says that the Mosaic Covenant is eternal.
Further, the covenant was not given to teach anyone to perform the eternal attributes of God. There are a number of reasons why the law was given, but this is not one of them.
The Bible often uses the same terms to describe the character of God as it does to describe the character of God's law, such as with it being holy, righteous, and good (Romans 7:12) or with justice, mercy, and faithfulness being weightier matters of the law (Matthew 23:23), and it could not accurately be described as that if it were not God's instructions for how to be a doer of those traits.
God's way is the way to know Him by being a doer of His character traits, such as in Genesis 18:19, God knew Abraham that he would teach his children and those of His household to walk in God's way by being a doer of righteousness and justice that the Lord might bring to him all that He has promised. In Exodus 33:13, Moses wanted God to be gracious to him by teaching him to walk in His way that he and Israel might know Him, in 1 Kings 2:1-3, God taught how to walk in His way through His law, and in Matthew 7:23, Jesus said that he would tell those who are workers of lawlessness to depart from hi because he never knew them, so the goal of the law is to teach us how to know God and Jesus through being a doer of His character traits, which is eternal life (John 17:3), and which is why Jesus said that the way to inherit eternal life is by obeying God's commandments (Luke 10:25-28, Matthew 19:17),
In Hebrews 1:3, the Son is the radiance of God's glory and the exact image of His character, which he expressed through his works by setting a sinless example for us to follow of how to walk in obedience to God's law.
In 1 Peter 1:16, we are told to be holy for God's is holy, which is quote from Leviticus where Good was given instructions for how to do that, so I don't see grounds for denying that it is God's instructions for how to act in accordance with His eternal holiness. The only way that we should no longer follow God's instructions for how to be holy if He is holy would be if God were to cease to be holy.
Lastly, I didn't suggest that God's graciousness was is superior to His righteousness. This you assumed. I said that grace was superior to the law.
God's law is His instructions for how to act in accordance with His righteousness, so that is the same. In any case, grace in not superior to law because the Bible is abundantly clear that God is gracious to us by teaching us to obey His law (Psalms 119:29, Exodus 33:13, Genesis 6:8-9, Romans 1:5, Ephesians 2:8-10, Titus 2:11-13).
Since no one will be justified by the law, but many are made righteous by grace, this can easily be seen to be the case.
The only way for someone to attain a character trait is through faith and what it means for someone to attain a character trait is for them to become a doer of that trait. For example, there are no amount of courageous works that someone is required to have done first in order to earn becoming courageous as the result, but rather the only way for someone to become courageous is through faith, but it would be contradictory for someone to become courageous apart from becoming a doer of courageous works, and the same is true for righteousness and every other character trait. So we do not earn our righteousness as the result of our obedience to God's law because it was never given as a means of earning our righteousness, but rather what it means to become righteous is to become s doer of righteous works in obedience to God's law, which is why the same faith by which we are declared righteous apart from works does not abolish our need to be a doer of righteous works in obedience to God's law, but rather our faith upholds it (Romans 3:27-31).