Wouldn't the title Mother of the Incarnate Christ solve the problem?
In a sense it would. But only if you define what you mean as "The Incarnate Christ". The Nestorians of the time would have agreed with that statement, even though they have a radically different view of what the Incarnation is than most Christians. They believed that Jesus was a divided man, in effect two people. That is what the Incarnation meant to them. It was one of the titles suggested (or something close), but was not chosen because it wasn't explicit enough.