If he really wants to atone, he should waive his double jeopardy defense when he confesses. Otherwise, it means nothing. You want to ease you guilty conscience? Fine. Justice wants its pound of flesh in return.
That's what I was thinking. He was acquitted at trial so even if he confesses, it means nothing. In fact, if he writes a book about it, he will make millions and not go to jail. The Son of Sam law will not apply since he was not found guilty.
My guess is he doesn't feel guilty, he just needs some cash. There are not a lot of endorsement opportunities for a guy who everyone thinks brutally murdered two people.