My mother, of blessed memory, always denied that Christmas was on December 25 because it replaced the Saturnalia. She pointed out what you just posted, namely that the Feast of the Annunciation had been celebrated even before Christmas and always on March 25. The calculation is easy to make. She said that her grandmother had told her this and she had heard it from hers and on back through the centuries.
Very interesting! You are the first person who has confirmed for me what I thought must exist -- a living tradition of why Christmas is celebrated when it is.