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a possible chance to demonstrate true repentance by confessing our wrongs and asking for forgiveness

I did a lot of thinking and reading on the topic of "forgiveness" once I found out about A with OM. A few days after the "too little, too late" bomb, I wrote my W a note, validating her thoughts, confirming that I had failed, committing that I would work to better myself and be more worthy, and that I wanted to improve our R. That was my one time only position statement, no talk of R or M ever again.
Of course, she openly mocks that note, but no matter, my position is known. But by mocking it, she was telling me she doesn't believe it. And this is what everyone here will keep telling you. It's what you do over an extended period of time, your true 180's that will be the proof. She may not even buy those, but that's all you've got. So knowing that, the confession of your wrongs isn't that important, certainly not to her. It will be the prolonged noticeable righting of those wrongs, and you don't need her to participate in that.
Now as for forgiveness. I will forgive my wife for the A, because if I don't, the anger and negativity will corrode my soul and affect me and make me bitter. So the act of forgiving is an act of self preservation. Now about being forgiven If you have recognized your faults, and have truly made changes to improve yourself, what more can you do? You should be of clear conscience. You can't forever blame yourself for your earlier ignorance of your faults. At that point, how much does someone else's approval matter? Point being, her forgiving you or not is not going to change your course of action to improve yourself. And if you follow through, then I think forgiveness of your faults becomes her issue, not yours.