"his head rolled limply to one side and his gaze passed to the audience" is a very nice turn, at first I was like, oh shit, are we the audience? Whew, no, just the animals.
"Outside the stars burned brightly with anticipation."
I was raised christian, and I really appreciate how much your story adds a tension that just isn't present in the tale as I've heard it told - reading the bible, there's never any real worry that jesus isn't going to make it, everybody knows he's born, he grows up and does miracles, he dies and gets resurrected, it's hard to feel like there's any ever real threat that he faces.
"Oh shit what if he's stillborn" is a very humanizing moment and I appreciate it.
I actually think you could have ended it right after "The woman murmured a desparate prayer and lifted her baby's head back upright." Just crop it off right there, and leave the audience to wonder.
I like this piece a lot.