But Silkie is right, you will need a special hearing of the zoning board. If it only costs $250, you are getting off easy. Where I live it is $800ish.
Edit: Your zoning is probably listed on your Township tax bill, which should have come recently since they are generally due March 31.
Baym:
Is that 800 for the hearing or 800 for the variance? either way thats pretty steep imho