His conception is different because the text says it is different.
His death is the same because the text says he was dead.
His birth was the same because the text says that "she gave birth," and as blue-duncan has so ably pointed out, her bleeding afterward made her unclean.
Now, we either use the text or we throw it out.
Pseudo-Aug., in App. s. 123: He, who by a touch could heal the severed limbs of others, how much more could He, in His own birth, preserve whole that which He found whole? In this parturition, soundness of the Mother’s body was rather strengthened than weakened, and her virginity rather confirmed than lost.
There you have it.