If you really don't want to claybar your car (which is prolly what you should do anyways) have you tried just waxing? A mild abrasive like wax might be enough. If that doesn't work, get some rubbing compound and a wheel. Either way, you're gonna have to put some work in.
And if you're cooking in the garage, perhaps it's the oils from foods which is falling onto your car. Don't you have a kitchen!?