You can't resolve anything if you try and resolve everything at one time. Lets start with your first claim and see which argument is better.
Your first claim was:
1. There are very reliable ways to know whether one section of the bible is unreliable. Especially for the NT. There is nothing textually or historically unique about this doctrinal passage. It has just as much textual and historical reliability as the Gospels and Paul's writings.
2. I have given the hard and inescapable numbers for NT reliability as a whole. It is about 95%. And even the critics admit no core doctrine (which this is) has any meaningful errors known.
3. This issues are so well established and by so many means that I can only fit one aspect of how this is done for just your initial claim in a whole post. We know this passage is textually reliable, unlike for example we know the last chapter of Mark is not. We know where the textual errors are, this is not a historical claim, so the next thing we should look at is whether what these verses teach is consistent with the rest of what Christ and the apostles taught. IOW is the idea that we must be born again consistent with the over all NT narrative. So lets see:
Ephesians 2:8-9 - For by grace are ye saved through faith; and that not of yourselves: [it is] the gift of God:
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1 Peter 1:23 - Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever.
Romans 6:23 - For the wages of sin [is] death; but the gift of God [is] eternal life through Jesus Christ our Lord.
Romans 6:6 - Knowing this, that our old man is crucified with [him], that the body of sin might be destroyed, that henceforth we should not serve sin.
John 3:1-8 - There was a man of the Pharisees, named Nicodemus, a ruler of the Jews:
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John 1:12 - But as many as received him, to them gave he power to become the sons of God, [even] to them that believe on his name:
John 1:1 - In the beginning was the Word, and the Word was with God, and the Word was God.
Joel 2:28-32 - And it shall come to pass afterward, [that] I will pour out my spirit upon all flesh; and your sons and your daughters shall prophesy, your old men shall dream dreams, your young men shall see visions:
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1 Corinthians 3:17 - If any man defile the temple of God, him shall God destroy; for the temple of God is holy, which [temple] ye are.
Romans 10:10 - For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.
Acts 22:16 - And now why tarriest thou? arise, and be baptized, and wash away thy sins, calling on the name of the Lord.
John 3:16 - For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
John 3:1-7 - There was a man of the Pharisees, named Nicodemus, a ruler of the Jews:
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Mark 16:16 - He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
2 Peter 3:9 - The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.
Romans 6:4 - Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
Romans 5:8 - But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.
Acts 2:38 - Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
John 3:36 - He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
Matthew 6:24 - No man can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon.
Matthew 3:13-17 - Then cometh Jesus from Galilee to Jordan unto John, to be baptized of him.
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2 Corinthians 5:17 - Therefore if any man [be] in Christ, [he is] a new creature: old things are passed away; behold, all things are become new.
There are actually more than thirty two verses that suggest we are to be born again to reach heaven. Every single Gospel contains them, John says more on it than the rest, and even most of Paul's works contain them. So you have two choices here.
1. The NT is reliable according to all the evidence and it says over and over we are to be born again.
2. The NT despite all the evidence is unreliable in every place it says we must be what you find inconvenient.
And BTW they did not require anyone be born again to join the church. Anyone could go to any church, especially those who had no faith. The Church in those early days is where you heard the word that led a person to becoming born again. Being born again is how church members became Christians not how they qualified to attend church.
Anyway before we move on to any other point you have to show me actual evidence and reasons to believe the bible was wrong or right except for where you don't like what it says. I have shown that it is historically reliable, it is textually reliable, we know where the errors are and even the critics agree core doctrine is free of them. You have to over turn all of this plus everything I will throw at you to make your first point even considerable.