You state the 'believe only' tradition well. I alluded to the fact in the article that πιστευω does not mean "believe" in the NT. It means "to commit" and is so translated by the KJV 7x. For example:
KJV John 2:24 But Jesus did not commit himself unto them, because he knew all men,
So a proper English translation of the text you quoted is, "Commit to the Lord Jesus Christ and thou shalt be saved"
This of course imlies more than intellectual assent. It implies total loyalty and support to Christ. As such πιστευω implies repentance.
The question will not be "how much sin did you commit", "how much good did you do", but "what did you do with my Son".
The question is likely to be a bit more specific than that. It will be, "Why did you turn the pardon available in My Son into a legal Acquittal"