It's been many years since I visited this subject. And I told myself to review it before posting and I didn't. I know the law was written down somewhere. That goes without saying. The obvious reference to it is made in scripture itself, as you point out. I'll have to reference some Messianic resources to answer your question. Maybe I just flat got it backwards and remember the argument wrong and it is the Rabbinal law that was oral. Makes more sense that way anyway.
I've debated this passage with many Messianics in past years and what I do remember is "the tradition of men, according to the elementary principles of the world" is talking about rabbinical add-on law, not the law of Moses itself, even though it is clear the debt of the law of Moses itself is not against us anymore either. For Paul to be speaking so negatively of the law of Moses itself does not fit. He would never do that. He did the exact opposite.
The judging that Paul is resisting is in regard to the rabbinical laws about how to observe the feasts and sabbaths of the law. Since the requirement to keep Moses' laws of Sabbaths and Feasts in the first place is now obsolete how much more so the rabbinical laws added on to them.
The Law of Moses, is against anyone who has ever sinned. Paul never speaks negatively of the Law. His point is that Man is what was wrong under the Law. What Paul says almost exclusively, is Him giving revelation into scripture and prophecy in the Ot. the thing is with the law of Moses, is this when it is written, it is for the very Purpose of Being a witness against the People it is given to. God tells Moses plainly " you are about to die, when you do this People will utterly turn away and turn to other gods and break My covenant, and provoke me to furious anger upon them and i will hide My face from them."
then Moses writes the Law, and tells the People " Place this law beside the ark of the testimony, and there it will remain as a witness against you." well God would come above the Mercy seat on the ark and commube with them, at His side, was the Law of Moses, continually accusing and testifying against sinners, it is Placed Beside the ark, for that Purpose where it would Be continually in the presence of the ark of the covenant. it is called the ark of the covenant, as soon as they place Gods commandments inside.
in revelation 5. A Lamb appears and aproaches the One sitting on the throne who has a Book in His right Hand, the book is sealed with seven seals. The Lamb who Has proven Worthy to open the Book, takes the Book from His hands...opens the seals.
this Little Book, is the Mosaic Law the witness constantly accusing Mankind at the side of Gods Presence. the Law itself is Good, for the sinners it is a death sentance. and doesnt offer Life to the transgressors. Jesus was perfect, when He was exalted He that fulfilled the Law of Moses, has Now Become One seated at Gods Side, who is a constant ADVOCATE for us, who is interceeding for us and Not accusing us. thats why Jesus is Pictured at the side of God, the Word of God seated at His side.
this in the Ot, is the book of the Law that was Beside Gods seat. paul always says the Law is Good righteous and Holy, we Mankind are the problem with the Law. it had a Purpose it still does, its Meant to Lead People to Christ when they realize they are condemned By the Law of Moses and Need a savior from its curse. He took the book of the Law of Moses away. and He tore the curtain in the temple so that we see the ark of the coveannt ( ten commandments) in the tabernacle in Heaven. and we then understand why its Now about " the commandments of God, and the testimony of Jesus Christ. ......and Not the Law of Moses.
the Law and Prophets were preached until John" since then the Kingdom of God is Preached......the Law is No More Preached aa the authority , it remains still in its entirety in order to reveal sin in Man and lead sinners to repentance through Jesus Christ it has its Purpose still.