IMO I think it's okay to acknowledge her birthday. If you don't it's going to be a repeat of what pushed her away in the first place. When you had your EA she felt that she couldn't trust you. All it would do is do more of the same. In what way can you show her "compassion" and understanding. And I'm not talking about constantly agreeing to what she says. You have to really seem like you understand her. If and when you talk, ask her questions, keep things light at first like a friend would.
Your W seems like she's still trying to sort things out in her head and needed you out of the picture because she was never given the tools to cope with conflict in a healthy way.
If she didn't tell you that your EA still bothered her even after 2 years, she isn't going to talk to a C. Maybe ask your C what you can do to re-establish trust with her and then when the opportunity presents itself, do it.
Right now it sounds like you're still trying to control the sitch and aren't sure if you're committed to fixing this M. You say how you want to save the M, then you mention how you have nothing to tie you down to move on. Did you ever think that maybe your W gets that vibe off of you? I mean that attitude is what made her leave in the first place. She felt that you felt she was replaceable. That's a huge fear to overcome for someone like her.
So maybe just be polite and acknowledge her b-day (she is your W after all), and not "expect" anything in return.
If you're not committed to re-establish the trust with your W and dedicate the many days/months whatever to it, then you might as well file right now and move on.
M-43 W-40 2D - 9 and 5
Emotion, yet peace. Ignorance, yet knowledge. Passion, yet serenity. Chaos, yet harmony. Death, yet a new life.