Granted that fact that it isn't a game could be enough to remove some of the confusion.
I really think you should change the name. If you go on a full out fight with Zynga, you won't find much sympathy I think.
That said, some very nice PR here, and you can probably look forward to some more PR once you acquiesce :)
Whatever the legal merits of protecting a name verses protecting a game, they get exactly zero sympathy from me for their intellectual property claims.
"Fuck you"