The language does not seem to address the consequences for a nonabjurer specialist incantrix.
The "forsaking other types of spells" seems to be either flavor or to be referring to the new prohibited spells. It does not say you lose your old specialization abilities.
Since it states the benefits of the incantrix pseudo specializing are "gaining all the benefits of specializing in a school" the question would seem to be one of stacking. By analogy clerics with two domains get bonus spells but only one bonus preparation slot total per level but have preparation choice between domains. That might be the best way to handle it but I can see it being handled differently with two bonus spells and one free spell must come from each school.