The brain cells of Janice would still consist of two X chromosomes meaning her sexual identity is female. As this is what you suppose 'radical feminists' base their theory on.. that female biological capabilities are responsible for identifying as female then gender identity would be determined completely by the social structure in which Janice has experienced.

As a result she may perceive herself as identifying as male of female depending on these experiences. This shows that depending on the societies gender normalities the results of Janices identity may be different.

As an incredibly simple example just for context she may have grown up in a house where in society A playing football and dressing in boys clothes were frowned up she may end up identifying as transgender in the future. However if Janice grew up in society B where those activities were accepted for girls to join she may not have ended up identifying as the opposite gender to her sex. Obviously there are many more factors that play in the real world but that is the general concept and perhaps if society were more accepting of people and abolished gender normalities could people feel comfortable in their own bodies.