There's a 2013 NPR interview with Kid Rock about the comparable problem of concert ticket scalping prices. His solution: do more shows in popular cities to satisfy demand; reserve a few premium seats and price them at scalping market prices so he's making a good overall profit; and (not applicable to shoes) bind the ticket to the buyer and require ID at the door.

https://www.npr.org/sections/money/2016/04/20/475023002/epis...