Even if you "mandate transparency," she can always go to the library or a friend's computer, and she can get another email address without you knowing.
You don't have to trust her, but keeping her under lock and key (eg, mandating transparency) isn't going to attract her to you. Mandating anything is just going to make her resent you.
Your idea of doing some kind of act of showing trust is nice, but are you ready to tell her that you trust her in honesty? I don't think you trust her yet (you will know when you do, because there will be a shift in your intimacy.)
I certainly don't blame you for needing some time to build that trust in her again, and any hint of her trying to contact OM likely brings you right back to square one. So, while you blame yourself for bringing you two back to square one, the reality is that she hasn't really kept up her end of the deal either.
You both need some time and breathing room for personal development, in my opinion. Don't be too hard on yourself, and embrace the pain of growth!
