I could be wrong about how this plays out, but, if I were in Belichick's place, one thing would start Mangini on the road to redemption with me: Confession.
That is, stop dancing around the topic with how much you regret things and how unfortunate it was the way things played out. Come clean and admit that you had a guy taping signals also, what other teams you knew were doing it, and how it was just one of many factors that went into preparing for a future opponent. Basically, help expose the myth that only the Patriots were doing this and it was a huge factor in their success.
I don't think making those statements could damage Mangini's career prospects more than they are already are. At least saying something more substantial will be better than these semi-annual "I hope we can reconcile some day" interview.
Edit to add: Mangini could also say how he reached out to Belichick to warn him, but didn't mention that Tannenbaum and the league office were also involved.