These types of people feed off of the reactions people have to their slights, insults, and lack of decency/respect .... unless the reactions become counter-productive in some way, or unexpectedly costly (the same with children, which is basically -- on some real level -- what these people are). That could mean simply ignoring them, or (inversely) perhaps even telling them to their face how badly they were raised (and suggesting they should try and overcome their bad upbringing, or something like that), and then regularly repeating that, a situation in which ignoring you will come at a high cost for them as you constantly remind them how you are able to assault them, while they just passively listen to it while pretending to ignore you.
That said, how much stress are you able to deal with in countering these kinds of people? Do you want to go down to their level?
Basically, trying to reason in any way with a neurotic, psychological minor is most likely bound to fail, as already baked into the cake by the very nature of the mental problem that gave rise to the unwished-for dynamic. If they were not able to figure on their own that they are acting dumb, then your protests are unlikely be have a remedial, educational effect.
I, therefore, feel that getting into head games of any kind would actually be counter-productive for you. Many Japanese act and react from rather immature, almost stuck in childhood, levels of emotional irrationality of the highest order.
To be clear: you are in an asynchronous (not on a level playing field) relationship, with you not knowing what cultural or culturally-induced (like being stuck in childish dynamics) mental issues they have. Your attempt to deal with things in a certain way may, therefore, be completely ineffective. You are coming at it from reason, she is coming at it from irrationality. How are you going to win at that game? You are dealing with stunted emotional development. The person needs therapy.
There is always the option of changing jobs, or thinking this through more to see if you can manage to come up with a strategy to deal with the situation. Unfortunately though, it is unlikely to be resolved through kindness (she'll feed off of that in a negative way that will be draining for you), so the strategy would most likely revolve around having to up the costs of her behavior.
You might want to read about parental approaches (or therapies) for defiant disorder (and the like) in children. Dealing with this level of consciousness is often only successful by raising the costs of a person's uncivil behavior. Only pure behavior-therapy -ype approaches normally work in these cases; a Socratic, or reasoned approach escapes them (being stuck as they are in irrationality).
Final word on this: getting ones ego out of the way (very hard to do) when being treated without civility is critical to manage the situation correctly. Reflecting on the mental prison this person is in and feeling sufficient compassion is also important. Remember, you wouldn't be too offended by a minor acting in such childish ways (which are frequently retaliatory, as well as attention-seeking). You are dealing with the equivalent of that here, so keep things in perspective and don't let her disturb your balance. You will have to be the adult in the house.
Welcome to Japan, and good luck!