What you don't realize is that we are freed from the letter of the law, because we follow the Spirit of life in Christ, which goes much deeper than the Old Covenant laws you are referring to. When you follow the Spirit, it covers those laws and more.
I agree that we should not follow the Law according to the letter. The distinction between following the letter of the law or the spirit of the law is not in regard to following different sets of laws, but in regard to the manner in which someone obeys it with respect to its intent, for example:
Leviticus 19:12 You shall not swear by my name falsely, and so profane the name of your God: I am the Lord.
Someone who is focused on obey the spirit of this law will understand that its intent is for us to not swear falsely, whereas someone who is focused on obeying the letter of this law exactly how it is written will understand that we can swear falsely just as long as we don't do so in God's name. Incidentally, this was the heart of Jesus was criticizing the Pharisees for doing in Matthew 23:16-22.
Furthermore, the Law is spiritual in that it has always intended to teach us deeper spiritual principles of which the listed laws are just examples, and of which are the character traits of God, such as holiness, righteousness, goodness, justice, mercy, faithfulness, love, joy, peace, patience, kindness, gentleness, and self-control. If we correctly understand a spiritual principle, then it will lead us to do things things that are examples of that principle in accordance with God's instructions for how to do that found in His Law, not away from doing those things. For example, if we correctly understand the principle of God's love, then it should lead us to express His love through our actions.
Likewise, when we have a character trait, then we will express it through our actions, so when God gives us His righteousness and declares us to be righteous, then He is also declaring us to be someone who expresses His righteousness through our actions in obedience to His instructions for how to do that found in His Law. We are not given the righteousness of God in order to hide it under a bushel, but in order to let it shine through our actions.
In Ezekiel 36:26-27, the Spirit has the role of lead us to obey the Law. In Romans 8:4-7, those who walk in the Spirit are contrasted with those who have a mind set on the flesh who refuse to submit to God's Law. In Galatians 5:19-22, everything listed as works of the flesh that are against the Spirit are also against the Mosaic Law, while all of the fruits of the Spirit are in accordance with it.