The only possibilities seem to be a timing attack, exploiting a bug or taking advantage of an implementation that puts the dividend value in the exception when dividing by zero. I'm not sure anyone will bother writing the timing attack since he apparently gives out no prize.
Unless there's something in Java that allows you to manipulate private copies of private variables without access to the stored values.
I'm familiar with Java, but not so familiar that I can state with authority that such a thing is impossible.