Your first sentence again fails to interact with the texts at issue, which are neither addressed to unbelievers nor simply warning of loss of fellowship.
As for the the flesh committing sin versus the new man, that is a distinction without a difference as concerns saving faith versus denying it. It is the heart where sin begins, (Mk. 7:21-23) and it is the error of certain gnostic antinomians to hold one may sin with his flesh without affecting his relationship with God. We are not to repent for having a sinful nature, but for yielding to it, and to wilfully live after the flesh, (Gal. 5:19-21) or to impenitently continue in a something which is manifestly sin and could repent from, (1Tim. 5:8) or to assent to a false gospel, (Gal. 5:1-4) is to deny the faith, and its benefits.
What you keep clinging to in order to justify the false teaching you are holding onto can be likened to the difference between Judas and Peter. Peter repented and came back to the Lord because he was genuine. Judas stood in the presence of Christ, witnessed the Spirit’s work and tasted of the kingdom, yet he turned back because he was not a true believer. He “betrayed” Christ, because he was not genuine. Such is the case of those who profess Christ and then deny Him today. They profess, but do not possess to know Jesus Christ, who is Eternal Life. “Whosoever believes in Christ has eternal life and shall never die.”