Sometimes the LRT works so well that the WAS pushes even harder to justify their decision to leave, and this can be anything that is considered as "testing" you. I have seen these manipulation attempts myself a few times with my wife. And I think you'll find in your situation that she is taking extremes to cover her own hurt feelings about leaving you.
You must not give in and must take the higher route every time. That means not falling for her games and never allowing yourself to get overly emotional in front of her. Anything you do to create contempt will hurt your chances so make the extra effort to stay strong even when you're hurting more than ever. Make it very hard for her to leave the "good guy" that gives her space and respects her decision to leave.
About the birthday....
Go ahead and get her a birthday card that isn't sentimental and sight it "Happy Birthday, 'your name'". You can even slip in some money or a gift card if you see fit but nothing that can be considered trying to buy her love. I'd put a limit of $50 if you think that's ok or depending on your situation nothing at all. It's up to you if you want to just call her but since she lives with you a card will do better. Though, I tend to believe turning the other cheek and giving and making a slight sacrifice without need for anything in return will set you apart and have the other person want to give you something for for your effort. I have done this before long ago with an ex just out of the goodness of my heart and it did bring her back.