There are always more options than it seems. Always. And that may be the only always.
Your wife's experience of you before the affair was not the best, her experience of you now is getting good. That needs to grow to a certain point for her ... probably ... before she'll give up the other guy.
I'm not a fan of the term cake-eating. It implies there is only one side to the story.
So...you need to build your friendship, build other aspects of the relationship before you would start the cutoffs.
It's fine, great if you initiate. It's not fine if you over-initiate. If she's accepting...it's working. Dont' try to fix the parts that aren't broken.
As the relationship grows, you want to test the waters. Pull back a bit....initiate less and see what she does. But not yet.
sg Love is PATIENT, love is KIND, LOVE never fails / DB since 2001