Taking care of your health is certainly a good idea, so don't let me put you off that.
I think you will find that while cancer may respond to certain diet changes, it will prove difficult to find anything that will affect benign tumors, especially an AN. An acoustic neuroma grows slowly, and appears for all intents and purposes to the body as normal tissue - your DNA, your cell surface proteins, your chemistry, etc. The best research so far suggests that one little regulatory mechanism is out of whack, leading to the continued growth of the cells that make up the tumor, but otherwise they are normal schwann cells. That means that anything that is good for you is good for your AN, and anything that would inhibit the AN will inhibit other healthy tissue as well.
I think your best bet is to get as healthy as you can, and avoid anything that makes the symptoms flare up. It is certainly possible to watch and wait and not have significant tumor growth for years, so it is worth trying. Best wishes!
Steve