Anne Catherine Emmerick means nothing?
Mary of Agreda means nothing?
Correct. They mean nothing from the standpoint of deriving theological conclusions from them.
1) Nobody knows for sure if they wrote everything in the works attributed to them.
2) Even if the visions are genuine, it's difficult to separate actual private revelation from interjections from their own minds.
There's a reason the Church fell short of canonizing them. It's because the Church did not wish to implicitly endorse everything in these works.
I'll go with the consensus of the Church Fathers, and Pope St. Gregory the Great, first. Even many otherwise-Modernist sources have come to the conclusion that the woman is most likely St. Mary Magdalene.