I'm Dr. Jackie, an interpersonal communication researcher/professor and relationship expert. And am so sorry you are in this "not knowing" situation. This must be extremely painful.
I think you already know the best answer for you. That is, emotionally you have been divorced for quite awhile. And I do not just mean as evidenced by your affairs. Your wife is not putting you off "because the dog is sick." She knows that both of you are "emotionally divorced." Fly to see her since she is not coming to see you. And sit down not at the bar or her residence but maybe a restaurant/coffee house and be clear. Tell her you appreciate her being there for you over the years while you moved back and forth and for being "such a sport" about living where she didn't want to. But also ask her if she does not also agree that your paths have veered so off course from where you started that surely making it official would make it less painful for the both of you a year, 2 years, 5 years, etc. down the road.
Unless she asks directly and you cannot feel you can lie to her, I wouldn't necessarily mention that you have met someone. That may rub salt into her wounds. Even if she mentions she met someone, realize she may say that to "save face" and to make it seem like she is not hurt. So I wouldn't divulge the information about the woman you met. Take the higher road because I think the pain will lessen faster if you can save the wounds from going as deeply as possible.
I hope that makes sense. And from what you have shared, I am guessing she will be reasonable enough to agree that your divorce was emanate a long time ago.
I'm going to send my phone and Skype information if you would like to discuss further according to JA rules. Let me know if I can help.
Thanks and please take care,