First you say no more cuddling and asking for sex, and then you plan to give her a birthday gift of sexy underwear?? Do you not realize that gift is the same as asking for sex??
It probably WILL go over like a lead balloon. So why do it? Save that gift for another time, maybe even pull it out as a surprise when SHE is in the mood.
It seems to me you backed off the sex for a bit once before, and she was asking for it within a few days. Seems like she wants it, but would rather have the ability to diminish its importance by acting like she did you a favor or it was easier to let you have your way. So, I agree with you that backing off a bit is a good idea. But she won't want to be seen as pursuing you all the time, even just for sex. How about this: Wait for her to initiate the next time, then you can initiate again, once. Then wait for her again.