Getting a variance is the best way to do it – as that makes it legal and will save you from problems down the road plus give you an exit strategy if you ever want to sell it.
Another option – and I’m not saying this would work – would be to advertise some product for sale on the premises, and claim that it is a premise sign. For example, if there was a Coke machine on the property, you could advertise Coke and claim you were doing it to sell more coke in the machine. It’s a grey area in many cities and states. Of course, you would be very limited on the types of advertisers you could do this with. But I’ve seen it done before.