All these replies seem to assume that repentance and faith come as a result of regeneration. At least one post specifically denies that regeneration and justification occur at the same time. I cannot reconcile this with the scripture.

The scripture says that believing in the Son of God gives life (regeneration):

"But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name." John 20:31

Believe in the Lord, and receive life. This seems beyond all controversy to me.

Paul says that the believer is risen into newness of life by faith:

"Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God," Col. 2:2.

Peter taught that our hearts are purified by faith:

"And God, which knoweth the hearts, bare them witness, giving them the Holy Ghost, even as he did unto us; And put no difference between us and them, purifying their hearts by faith."

This is why clearly people were said to be born again or regeneration by the gospel. It is only when we believe the gospel that we are regenerated:

"For though ye have ten thousand instructers in Christ, yet have ye not many fathers: for in Christ Jesus I have begotten you through the gospel."

"Seeing ye have purified your souls in obeying the truth through the Spirit unto unfeigned love of the brethren, see that ye love one another with a pure heart fervently: Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever."