It's a compromise. W has flatly refused actual no contact.
It is better than the agreement we have now.
I guess that begs the question. If she is unwilling to do full no-contact, what can I infer from that and what is my next step?
You infer -- and you say to her -- "I can only infer then that you are still in contact with her, or you want to be ABLE to continue contact, in which case I guess I have my answer. I'm not willing to live in an open marriage."
There's no room for compromise when it comes to separating the addict from the source of their addiction (and make no mistake, affairs are HIGHLY addictive. Just Google "phenylethlamine addiction brain" to learn more. It's what made an otherwise sane, intelligent female astronaut drive from TX to FL, wearing an adult diaper, so that she wouldn't have to stop at rest areas and she could get there sooner to avenge her man. It's what makes highly-successful businesspeople and professionals throw away their careers.
You can't allow the pyromaniac to just keep a FEW of the matches in the home, nor the newly-recovering alcoholic just a FEW bottles of booze, as a "compromise."