There's never a perfect answer, but I think that validation and apology are good go-tos.
Like you, your wife was feeling relaxed and connected to you until the intrusive memory of your affair intervened. That's every bit as frustrating and disappointing for her as it is for you, but that's where your agendas diverge. You want to try to fix it, to prove that you're finally here to do the work. She needs you to acknowledge that you can't fix it, that you so thoroughly blew your chances at honesty that now the words you're offering are meaningless. You built this hell and put her in it, and now your job is to live there with her until she's ready to decide her path out.
This can be hard for a solutions-based person to hear, but it's too early to be working towards solutions. You're a few steps back from that, at fundamental acknowledgment. Contrary to what you said, her talking to you obviously is pointless. What good are the reassurances and promises of a liar? Even when you're not lying, how could she possibly tell?
IMO, the right thing to do was to say that you could see how the memory of what you did was hitting her, and that you would never be able to express how sorry you are for destroying her trust, both with your decision to cheat and your decision to lie. Then shut up and wait. Don't try to persuade her of how different you are now and how ready you are to change. The way you show that change is happening is by resisting the impulse to do the same things you did before (or make the same promises you've always made).
Just tell her you're sorry, and listen. Listening means giving up on any expectation of progress towards your goals. Simply sit in the reality. If she says your apology is meaningless, tell her you understand that you fucked things up to the level where she can't believe you. If she calls the entire discussion pointless, tell her you know that it will be a long time before you even have a right to hope that she'll feel differently.
Seeing her pain isn't synonymous with identifying that she needs to talk. She might just need you to recognize and accept your responsibility for creating that pain.
[This message edited by BraveSirRobin at 7:38 PM, July 25th (Saturday)]