There is absolutely no reason people need your physical address unless they are going to send someone around. I have the same thing with no mail at the house. If they demand a physical, I make 'em happy with the address of the post office and change the "PO Box" to "Apt", it works 90% of the time and passes credit card screening.
They can feel satisfied they can send some goons over, and I can feel satisfied they will find a nice brick bulding...