You know the one problem with all of this; by showing that jobs could be transferred, and a sister who could be willing to transfer.... this shouldn't be a problem.
Honestly, what the author should have done is instead had an object that could give a class instead of such a transfer.
Hell, the father should have just awakened her class himself with this method (like, with his status, he wouldn't know of it?). After all, if she's found not to be of the same job, it'd be dangerous for his family and nobles should be willing to cover up shame like that.
Sorry for the rant; but the author should have thought of this more.