Actually, in the GN, when he goes for his costume that's stashed in the alley so he can change into it, the shoes are with it. So he does wear different shoes when he's in hobo mode. They look brown instead of black in the opening panels - might still be elevators of course, but are at least physically a different pair, so who knows.

Thank you so much - it's such a fantastic picture, and gift art just makes me happier than Ican express. :D