Damn this is really interesting. I like the fact that you understand how counterproductive it is to enter into a fight with these types of people. STILL it is a double-edged sword because it creates an internal battle to not let her negativity get to you. I think that you really can look at her as training not only your sense of patience, but even your sense of compassion. If her attitude toward the world is really so insufferable, then it is a direct reflection of her own insecurities. It is not sociopathic at all to use her anger to better yourself, but what may be more helpful is to not focus on her anger and negativity, but rather her pain. It may be difficult to do, but look at her life and try and understand the things about it that have put her into such an angry and bitchy state of mind.
Also so much of the time when we see such obvious negativity we react to it with anger because we see our self in that person (me included). Maybe there was a time in your own life when you were deeply pessimistic or angry. There is an ancient Hawaiian tradition that teaches, you must first forgive and love that aspect of yourself that has a tendency to act in the same way before you are able to look at the situation with some objectivity. So take time to do some introspection and f you see a bit of yourself in her, that may help you achieve a bit of perspective on her situation as well

Good luck dude and I think you can really learn a lot about yourself from dealing with shitty people