By faith, Noah. By faith, Moses. By faith ... so says Hebrews chapter 11 with marvelous repetition. This is the way, truth, and life: My righteous one shall live by faith. Christianity declares that the Biblical way, truth, and life is the faith of the Son of God:
I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me. - Galatians 2:20
Noah found grace with God and he and his family were saved. God made His covenant with Noah and, through Noah, spared the earth from a total desolation of life. In constructing the ark Noah condemned the world and there is no biblical data suggesting that he tried to convince any other people to get in the ark and be saved. 2 Peter 2:5 calls Noah a "proclaimer" of righteousness with no other details about the content or method of his proclamation. The idea that Noah preached to others a way, truth, and life by which they might be saved is based in Jewish tradition and not the Biblical text. More likely it was the proclamation of obedient faith in God's righteousness according to which he built the ark and condemned the world, which is a type of salvation of which Christ is the anti-type.
Moses was the beginning of a covenant between God and man and was designed to be a stumbling block to the sinful heart of man, which desires to establish it's own righteousness. It was, in every facet, a ministry of condemnation rather than of life because only perfect obedience maintained life. In disobedience a death was required; either that of the sinner or a propitiatory sacrifice. Access to God through this covenant was only ever through faith in the operation of God and not the doing itself.
The six verses listed at the end of OP (I am sure that many others are in the arsenal) are all under the context of the Levitical priesthood (see especially Malachi) in the Mosaic covenant:
And ye shall know that I have sent this commandment unto you, that my covenant might be with Levi, saith the LORD of hosts. My covenant was with him of life and peace; and I gave them to him for the fear wherewith he feared me, and was afraid before my name. The law of truth was in his mouth, and iniquity was not found in his lips: he walked with me in peace and equity, and did turn many away from iniquity. For the priest's lips should keep knowledge, and they should seek the law at his mouth: for he is the messenger of the LORD of hosts. But ye are departed out of the way; ye have caused many to stumble at the law; ye have corrupted the covenant of Levi, saith the LORD of hosts. Therefore have I also made you contemptible and base before all the people, according as ye have not kept my ways, but have been partial in the law. - Malachi 2:4-9
Under the Mosaic covenant the pathway to God (the way, truth, and life) was through faithful obedience to the Law and, failing that, faithful sacrifice at the temple. Much more was included such as observing various feasts and regular offerings but priestly service in the temple was central and critical. It required faith to attempt obedience, faith to admit failure, faith to appeal through sacrifice, and faith that God would keep His word and forgive through that mechanism.
Christianity claims nothing different except that all the mechanism has been fulfilled for us by the Son of God; humbling Himself to be born under the Law and to redeem those under the Law. It is His faith that is the way, the truth, and the life. When a person, convinced of their sin, repents of it and calls on the name of the Lord a new covenant is entered. It is not like the Old Covenant:
Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah: Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD: But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more. - Jeremiah 31:31-34
Under the New Covenant the Spirit of God, the Spirit of Christ, takes up residence within a believer. One of the ways that the fruit (the produce) of this new Spirit manifests is faith. "The life they now life is lived by faith of the Son of God because Christ lives in them" says the apostle Paul. This is the manner in which Jesus is the way, truth, and life. Faith in God, just as it has always been. The difference being that every other prophet and holy man that God ever spoke through were types and shadows of the fulfillment, which is Christ Jesus our Lord.
Those who cling to the Old Covenant must wrestle with the fact that the way, truth, and life represented therein has been gone for some 2000 years. Faith in the operation of God through the Temple and the Levitical priesthood has been removed, rendered impossible. There is absolutely no way for atonement to be made for sin on an altar in a temple that does not exist. This is the heart of Jesus' claim in John 14:
Let not your heart be troubled: ye believe in God, believe also in me. In my Father's house are many mansions: if it were not so, I would have told you. I go to prepare a place for you. And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also.And whither I go ye know, and the way ye know. Thomas saith unto him, Lord, we know not whither thou goest; and how can we know the way? Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me. If ye had known me, ye should have known my Father also: and from henceforth ye know him, and have seen him. - John 14:1-7
He is the Way: He is the Temple, made without hands, wherein God dwells among His people. The access to God for both offering and sacrifice. He is the great and faithful High Priest, performing, in Himself for us, all that the Law requires. He is the mercy seat. He is the ark. He is both Shepherd and gate of the sheep.
He is the Truth: He is the Logos (the rational mind of God), the Word of God who is God, residing in humanity. The law of truth was in his mouth, and iniquity was not found in his lips. He is God's law written in our inward parts and the Spirit of Truth facilitating obedience to the Law's righteous requirements.
He is the Life: All that the Law was unable to accomplish because of the weakness of the flesh, Jesus did and is. In Him was life and that life was the light of men. He is the brazen serpent held up on a pole that everyone who sees Him and believes may live.
Judaism no longer has access to God through the Mosaic covenant because it has been taken away and nailed to the cross. There is no temple in Jerusalem and no altar. Atonement can no longer be made for the sins of the people. Their house is left unto them desolate and will remain so until they say "Blessed is He (Jesus) that comes in the Name of the LORD". Here I recommend the entirety of Psalm 118.
The LORD hath chastened me sore: but he hath not given me over unto death. Open to me the gates of righteousness: I will go into them, and I will praise the LORD: This gate of the LORD, into which the righteous shall enter. I will praise thee: for thou hast heard me, and art become my salvation. The stone which the builders refused is become the head stone of the corner. This is the LORD'S doing; it is marvellous in our eyes. This is the day which the LORD hath made; we will rejoice and be glad in it. Save now, I beseech thee, O LORD: O LORD, I beseech thee, send now prosperity. Blessed be he that cometh in the name of the LORD: we have blessed you out of the house of the LORD. God is the LORD, which hath shewed us light: bind the sacrifice with cords, even unto the horns of the altar. Thou art my God, and I will praise thee: thou art my God, I will exalt thee. O give thanks unto the LORD; for he is good: for his mercy endureth for ever. - Psalm 118:18-29