Suppose a girl is being abused by her uncle. She doesn't experience it as terrible but she wants it to stop. But she doesn't want to face a formal investigation, which involves endless interrogations for her, embarrassing publicity, family strife, and perhaps sending her uncle to prison for 10 years. If she knew there could be a way of handling the situation privately in accord with her needs and wishes, she may be more likely to report it and get it to stop.

This scenario sounds a bit fantastical; the rape survivor who doesn't go to the cops isn't doing it because they "[didn't] experience it as terrible" and want to protect their rapist, it's because doing so puts them on the firing line and brings back all the trauma with the added benefit of a negligible chance of actually seeing justice. I would know here; one of my childhood friends was raped by some freak when she was a little girl, and even though she managed to grow up healthy despite it that single attack still left a lot of deep psychological scars. And that is a best-case scenario; a girl like you describe is trapped with their rapist and is unlikely to even be willing to tell their parents what happened, which means they will be raped over and over while being forced to pretend nothing is wrong.

It's not the stigma against pedophiles which hurts these children... it's the pedophiles who rape them.

I realize you claim not to have hurt a child, and if it's true I'm certainly glad about that, but there really is no comparison between the inconvenience of sexual frustration / possible police investigation and being raped. "Coming out" and making sure that society can protect itself is the only moral thing to do if you really are sincere here; the cost of raping children or providing demand for pornography in which children are raped is so much higher than any price a person can pay socially or legally that you would absolutely come out ahead no matter what happened. The highest ideal of a civilized person is to do the right thing even if it's painful, and that means having the courage to accept the consequences of your actions.